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Journal articles on the topic 'Transcendence of the power series'

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Published: 4 June 2021

Last updated: 13 February 2022

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1

Wu, Qiang, and Ping Zhou. "Transcendence of some multivariate power series." Frontiers of Mathematics in China 9, no. 2 (2014): 425–30. http://dx.doi.org/10.1007/s11464-014-0363-9.

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2

Karadeniz Gözeri, Gül, Ayten Pekin, and Adem Kılıçman. "On the transcendence of some power series." Advances in Difference Equations 2013, no. 1 (2013): 17. http://dx.doi.org/10.1186/1687-1847-2013-17.

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3

Allouche, J. P. "Transcendence of formal power series with rational coefficients." Theoretical Computer Science 218, no. 1 (1999): 143–60. http://dx.doi.org/10.1016/s0304-3975(98)00256-4.

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4

Allouche, J. P., D. Gouyou-Beauchamps, and G. Skordev. "Transcendence of Binomial and Lucas' Formal Power Series." Journal of Algebra 210, no. 2 (1998): 577–92. http://dx.doi.org/10.1006/jabr.1998.7606.

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5

Borwein, Peter, and Michael Coons. "Transcendence of power series for some number theoretic functions." Proceedings of the American Mathematical Society 137, no. 04 (2008): 1303–5. http://dx.doi.org/10.1090/s0002-9939-08-09737-2.

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6

COONS, MICHAEL. "THE TRANSCENDENCE OF SERIES RELATED TO STERN'S DIATOMIC SEQUENCE." International Journal of Number Theory 06, no. 01 (2010): 211–17. http://dx.doi.org/10.1142/s1793042110002958.

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We prove various transcendence results regarding the Stern sequence and related functions; in particular, we prove that the generating function of the Stern sequence is transcendental. Transcendence results are also proven for the generating function of the Stern polynomials and for power series whose coefficients arise from some special subsequences of Stern's sequence.

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7

Sun, Hae-Sang. "Borel’s conjecture and the transcendence of the Iwasawa power series." Proceedings of the American Mathematical Society 138, no. 06 (2010): 1955–63. http://dx.doi.org/10.1090/s0002-9939-10-10287-1.

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8

COONS, MICHAEL, and YOHEI TACHIYA. "TRANSCENDENCE OVER MEROMORPHIC FUNCTIONS." Bulletin of the Australian Mathematical Society 95, no. 3 (2017): 393–99. http://dx.doi.org/10.1017/s0004972717000193.

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In this short note, considering functions, we show that taking an asymptotic viewpoint allows one to prove strong transcendence statements in many general situations. In particular, as a consequence of a more general result, we show that if$F(z)\in \mathbb{C}[[z]]$is a power series with coefficients from a finite set, then$F(z)$is either rational or it is transcendental over the field of meromorphic functions.

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9

Ammous, B., S. Driss, and M. Hbaib. "Continued Fractions and Transcendence of Formal Power Series Over a Finite Field." Mediterranean Journal of Mathematics 13, no. 2 (2014): 527–36. http://dx.doi.org/10.1007/s00009-014-0507-x.

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10

Ammous, Basma, Sana Driss, and Mohamed Hbaib. "A transcendence criterion for continued fraction expansions in positive characteristic." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 237–42. http://dx.doi.org/10.2298/pim141206012a.

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11

Gouadri, Marwa, та Mohamed Hbaib. "Transcendental continued β-fraction with quadratic pisot basis over Fq((x-1))". Filomat 33, № 14 (2019): 4585–91. http://dx.doi.org/10.2298/fil1914585g.

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Let Fq be a finite field and Fq((x-1)) is the field of formal power series with coefficients in Fq. Let ??Fq((x-1)) be a quadratic Pisot series with deg(?) = 2. We establish a transcendence criterion depending on the continued ?-fraction of one element of Fq((x-1)).

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12

Coons, Michael. "Extension of Some Theorems of W. Schwarz." Canadian Mathematical Bulletin 55, no. 1 (2012): 60–66. http://dx.doi.org/10.4153/cmb-2011-037-9.

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AbstractIn this paper, we prove that a non–zero power series F(z) ∈ ℂ[[z]] satisfyingwhere d ≥ 2, A(z), B(z) ∈ C[z] with A(z) ≠ 0 and deg A(z), deg B(z) < d is transcendental over ℂ(z). Using this result and a theorem of Mahler’s, we extend results of Golomb and Schwarz on transcendental values of certain power series. In particular, we prove that for all k ≥ 2 the series is transcendental for all algebraic numbers z with |z| < 1. We give a similar result for . These results were known to Mahler, though our proofs of the function transcendence are new and elementary; no linear algebra or

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13

Fleischmann, Peter, and Chris Woodcock. "Stable transcendence for formal power series, generalized Artin-Schreier polynomials and a conjecture concerning p-groups." Bulletin of the London Mathematical Society 50, no. 5 (2018): 933–44. http://dx.doi.org/10.1112/blms.12197.

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14

KANEKO, HAJIME. "On the beta-expansions of 1 and algebraic numbers for a Salem number beta." Ergodic Theory and Dynamical Systems 35, no. 4 (2014): 1243–62. http://dx.doi.org/10.1017/etds.2013.99.

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AbstractWe study the digits of $\beta $-expansions in the case where $\beta $ is a Salem number. We introduce new upper bounds for the numbers of occurrences of consecutive 0s in the expansion of 1. We also give lower bounds for the numbers of non-zero digits in the $\beta $-expansions of algebraic numbers. As applications, we give criteria for transcendence of the values of power series at certain algebraic points.

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15

Denis, Laurent. "Méthodes fonctionnelles pour la transcendance en caractéristique finie." Bulletin of the Australian Mathematical Society 50, no. 2 (1994): 273–86. http://dx.doi.org/10.1017/s0004972700013733.

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There are essentially two ways to obtain transcendence results in finite characteristic. The first, historically, is to use Ore's lemma and to prove that a series whose coefficients satisfy well-behaved divisibility properties cannot be a zero of an additive polynomial. This method is of the same kind as the method of p–automata. The second one is to try to imitate the usual methods in characteristic zero and to do transcendence theory with t–modules analogously to what we can do with algebraic groups. We want to show here that transcendence results over Fq(T) can also be obtained with the hel

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16

Boyadzhiev, Khristo N. "A series transformation formula and related polynomials." International Journal of Mathematics and Mathematical Sciences 2005, no. 23 (2005): 3849–66. http://dx.doi.org/10.1155/ijmms.2005.3849.

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We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions forλ>0of the incomplete gamma functionγ(λ,x)and of the Lerch transcendentΦ(x,s,λ). In one particular case, our formula reduces to a series transformation formula which appears in the works of Ramanujan and is related to the exponential (or Bell) polynomials. Another particular case, based on the geometric series,

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17

Schrock, Chad. "The Borderlands of Belief: Phil Rickman’s Merrily Watkins Mysteries." Christianity & Literature 67, no. 4 (2018): 689–708. http://dx.doi.org/10.1177/0148333117695811.

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Merrily Watkins is a highly unconventional Anglican priest and exorcist, and her eponymous mystery series represents the church she serves as hopelessly out of touch culturally and morally. Such distance from conventional Christianity manifests a sensibility increasingly called postsecular: distaste for the power moves of organized religion alongside acknowledgement that the ongoing contemporary quest for and experience of transcendent meaning disproves triumphalist secularization. The series prioritizes Christianity within this anti-dogmatic religious landscape because of Christianity’s stabl

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18

Voynova, Ya A., A. D. Koralkov, and E. M. Оvsiyuk. "Scalar particle with the Darwin – Cox intrinsic structure in the external Coulomb field." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (2020): 467–78. http://dx.doi.org/10.29235/1561-2430-2019-55-4-467-478.

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The generalized Klein – Fock – Gordon equation for a particle with the Darwin–Cox structure allowing for a charge distribution of a particle over a sphere of finite radius is studied with regard to the external Coulomb field. The separation of variables is carried out, the obtained radial equation is significantly more complicated than the equation in the case of ordinary particles, it has essentially singular points r = 0 of rank 3, r = ∞ of rank 2 and 4 regular singular points. In the case of a minimum orbital momentum l = 0, the structure of singularities is simplified: there are essentiall

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19

Penelhum, Terence. "The Loss and Recovery of Transcendence: The Will to Power and the Light of HeavenJohn C. Robertson Princeton Theological Monograph Series, no. 39 Allison Park, PA: Pickwick, 1995. xvii + 108 pp., $14.00 paper." Dialogue 37, no. 3 (1998): 587–88. http://dx.doi.org/10.1017/s0012217300020540.

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20

Waitt, Gordon. "The Sydney 2002 Gay Games and Querying Australian National Space." Environment and Planning D: Society and Space 23, no. 3 (2005): 435–52. http://dx.doi.org/10.1068/d401.

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In what ways did Sydney's Gay Games reinvent the Australian nation? In this paper I set out to examine this question by drawing upon the idea that sports and parades of athletes during opening ceremonies have been definitive moments for the Australian nation. I investigate the social terrains or bodyscapes invoked by sporting gay pride during the participants' parade at the opening ceremony and sports venues of the Sydney 2002 Gay Games. This enables insights into whether these spaces subverted the heteronormativity of sporting bodies that are metaphors for Australian national space. I centre

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21

King-Farlow, John. "Comptes rendus / Reviews of books: The Loss and Recovery of Transcendence: The Will to Power and the Light of Heaven John C. Robertson, Jr. Princeton Theological Monograph Series, 39 Allison Park, PA: Pickwick Publications, 1995. xvii + 108 p." Studies in Religion/Sciences Religieuses 29, no. 3 (2000): 367–68. http://dx.doi.org/10.1177/000842980002900320.

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22

Duverney, Daniel, Keiji Nishioka, Kumiko Nishioka, and Iekata Shiokawa. "Transcendence of Jacobi's theta series." Proceedings of the Japan Academy, Series A, Mathematical Sciences 72, no. 9 (1996): 202–3. http://dx.doi.org/10.3792/pjaa.72.202.

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23

Zhu, Yao Chen. "Transcendence of Certain Trigonometric Series." Acta Mathematica Sinica 18, no. 3 (2002): 481–88. http://dx.doi.org/10.1007/s10114-002-0183-9.

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24

Koral’kov, A. D., E. M. Ovsiyuk, V. V. Kisel, A. V. Chichurin, Ya A. Voynova, and V. M. Red’kov. "Spinless Particle with Darwin–Cox Structure in an External Coulomb Field." Nonlinear Phenomena in Complex Systems 23, no. 4 (2020): 357–73. http://dx.doi.org/10.33581/1561-4085-2020-23-4-357-373.

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Generalized Klein–Fock–Gordon equation for a spinless particle with the Darwin–Cox structure, which takes into account distribution of the electric charge of a particle inside a finite spherical region is studied in presence of an external Coulomb field. There have been constructed exact Frobenius type solutions of the derived equations, convergence of the relevant power series with 8-term recurrent relations has been studied. As an analytical quantization rule is taken the so-called transcendency conditions. It provides us with a 4-th order algebraic equation with respect to energy values, wh

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25

Weatherby, Chester. "Transcendence of multi-indexed infinite series." Journal of Number Theory 131, no. 4 (2011): 705–15. http://dx.doi.org/10.1016/j.jnt.2010.11.003.

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26

Kumar, Veekesh. "A transcendence criterion for Cantor series." Acta Arithmetica 188, no. 3 (2019): 269–87. http://dx.doi.org/10.4064/aa170803-19-5.

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27

Hančl, Jaroslav, and Pavel Rucki. "The Transcendence of Certain Infinite Series." Rocky Mountain Journal of Mathematics 35, no. 2 (2005): 531–37. http://dx.doi.org/10.1216/rmjm/1181069744.

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28

Woodcock, Christopher F., and Habib Sharif. "On the transcendence of certain series." Journal of Algebra 121, no. 2 (1989): 364–69. http://dx.doi.org/10.1016/0021-8693(89)90072-0.

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29

Sjö, Sofia. "Postmodern messiahs: the changing saviours of contemporary popular culture." Scripta Instituti Donneriani Aboensis 21 (January 1, 2009): 196–212. http://dx.doi.org/10.30674/scripta.67351.

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The messiah myth is alive and well in the modern world. Contemporary science fiction film has taken the myth to heart and given us an endless stream of larger than life heroes. The heroes of the present are, however, not exactly the same as the heroes of the past. A changing world demands new things of its saviours. Using a textual and narrative analysis based on insights gained from feminist film theory and cultural studies, this article looks closely at the messiah theme in science fiction films and TV series from the last three decades. The study explores the changes that have occurred in r

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30

André, Yves. "Arithmetic Gevrey series and transcendence. A survey." Journal de Théorie des Nombres de Bordeaux 15, no. 1 (2003): 1–10. http://dx.doi.org/10.5802/jtnb.383.

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31

HANČL, JAROSLAV, and JAN ŠTĚPNIČKA. "ON THE TRANSCENDENCE OF SOME INFINITE SERIES." Glasgow Mathematical Journal 50, no. 1 (2008): 33–37. http://dx.doi.org/10.1017/s0017089507003989.

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AbstractThe paper deals with a criterion for the sum of a special series to be a transcendental number. The result does not make use of divisibility properties or any kind of equation and depends only on the random oscillation of convergence.

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32

Nyblom, M. A. "A Theorem on Transcendence of Infinite Series." Rocky Mountain Journal of Mathematics 30, no. 3 (2000): 1111–20. http://dx.doi.org/10.1216/rmjm/1021477261.

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33

RAM MURTY, M., and CHESTER J. WEATHERBY. "ON THE TRANSCENDENCE OF CERTAIN INFINITE SERIES." International Journal of Number Theory 07, no. 02 (2011): 323–39. http://dx.doi.org/10.1142/s1793042111004058.

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We investigate the transcendental nature of the sum [Formula: see text] where A(x), B(x) are polynomials with algebraic coefficients with deg A < deg B and the sum is over integers n which are not zeros of B(x). We relate this question to the celebrated conjectures of Gel'fond and Schneider. In certain cases, these conjectures are known, and this allows us to obtain some unconditional results of a general nature.

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34

BUNDSCHUH, PETER. "TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF SERIES RELATED TO STERN'S SEQUENCE." International Journal of Number Theory 08, no. 02 (2012): 361–76. http://dx.doi.org/10.1142/s1793042112500212.

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In this same journal, Coons published recently a paper [The transcendence of series related to Stern's diatomic sequence, Int. J. Number Theory6 (2010) 211–217] on the function theoretical transcendence of the generating function of the Stern sequence, and the transcendence over ℚ of the function values at all non-zero algebraic points of the unit disk. The main aim of our paper is to prove the algebraic independence over ℚ of the values of this function and all its derivatives at the same points. The basic analytic ingredient of the proof is the hypertranscendence of the function to be shown

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35

Kurosawa, Takeshi. "Transcendence of certain series involving binary linear recurrences." Journal of Number Theory 123, no. 1 (2007): 35–58. http://dx.doi.org/10.1016/j.jnt.2006.05.019.

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36

Nyblom, M. A. "A Theorem on Transcendence of Infinite Series II." Journal of Number Theory 91, no. 1 (2001): 71–80. http://dx.doi.org/10.1006/jnth.2001.2672.

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37

Hallanger, Nathan J. "CTNS Science and Transcendence Advanced Research Series Update." Theology and Science 6, no. 2 (2008): 127–28. http://dx.doi.org/10.1080/14746700801976817.

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38

Forrester, Peter J., and Anthony Mays. "Finite-size corrections in random matrix theory and Odlyzko’s dataset for the Riemann zeros." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2182 (2015): 20150436. http://dx.doi.org/10.1098/rspa.2015.0436.

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Odlyzko has computed a dataset listing more than 10 9 successive Riemann zeros, starting from a zero number to beyond 10 23 . This dataset relates to random matrix theory as, according to the Montgomery–Odlyzko law, the statistical properties of the large Riemann zeros agree with the statistical properties of the eigenvalues of large random Hermitian matrices. Moreover, Keating and Snaith, and then Bogomolny and co-workers, have used N × N random unitary matrices to analyse deviations from this law. We contribute to this line of study in two ways. First, we point out that a natural process to

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39

DUVERNEY, DANIEL. "Transcendence of a fast converging series of rational numbers." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 2 (2001): 193–207. http://dx.doi.org/10.1017/s0305004100004783.

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40

Amou, Masaaki, and Masanori Katsurada. "Differential transcendence of a class of generalized Dirichlet series." Illinois Journal of Mathematics 45, no. 3 (2001): 939–48. http://dx.doi.org/10.1215/ijm/1258138161.

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41

KUMAR, VEEKESH, and BILL MANCE. "ON THE TRANSCENDENCE OF CERTAIN REAL NUMBERS." Bulletin of the Australian Mathematical Society 99, no. 03 (2019): 392–402. http://dx.doi.org/10.1017/s0004972719000194.

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In this article, we prove the transcendence of certain infinite sums and products by applying the subspace theorem. In particular, we extend the results of Hančl and Rucki [‘The transcendence of certain infinite series’, Rocky Mountain J. Math. 35 (2005), 531–537].

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42

Holmberg, David. "Transcendence, Power and Regeneration in Tamang Shamanic Practice." Critique of Anthropology 26, no. 1 (2006): 87–101. http://dx.doi.org/10.1177/0308275x06061485.

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43

Trojovská, Eva, and Pavel Trojovský. "Schanuel’s Conjecture and the Transcendence of Power Towers." Mathematics 9, no. 7 (2021): 717. http://dx.doi.org/10.3390/math9070717.

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We give three consequences of Schanuel’s Conjecture. The first is that P(e)Q(e) and P(π)Q(π) are transcendental, for any non-constant polynomials P(x),Q(x)∈Q¯[x]. The second is that π≠αβ, for any algebraic numbers α and β. The third is the case of the Gelfond’s conjecture (about the transcendence of a finite algebraic power tower) in which all elements are equal.

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44

Hanafi, Hassan. "The Revolution of The Transcendence." Kanz Philosophia : A Journal for Islamic Philosophy and Mysticism 1, no. 2 (2011): 23. http://dx.doi.org/10.20871/kpjipm.v1i2.12.

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Contrary to the general and common idea that Islam etymologically means submission, surrendering, servitude or even slavery, this paper tries to prove just the opposite, that Islam is a protest, an opposition and a revolution. The term Aslama, in fact, is ambiguous. It means to surrender to God, not to yield to any other power. It implies a double act : ﬁrst, a rejection of all non-Transcendental yokes; and second, an acceptance of the Transcendental Power. Islam, by this function, is a double act of negation and afﬁrmation. This double act is expressed in the utterance “I witness that there i

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45

Kolouch, Ondřej, and Lukáš Novotný. "Diophantine Approximations of Infinite Series and Products." Communications in Mathematics 24, no. 1 (2016): 71–82. http://dx.doi.org/10.1515/cm-2016-0006.

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Abstract This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos’ results on irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.

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46

Aydin, Ciano, and Peter-Paul Verbeek. "Transcendence in Technology." Techné: Research in Philosophy and Technology 19, no. 3 (2015): 291–313. http://dx.doi.org/10.5840/techne2015121742.

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According to Max Weber, the “fate of our times” is characterized by a “disenchantment of the world.” The scientific ambition of rationalization and intellectualization, as well as the attempt to master nature through technology, will greatly limit experiences of and openness for the transcendent, i.e. that which is beyond our control. Insofar as transcendence is a central aspect of virtually every religion and all religious experiences, the development of science and technology will, according to the Weberian assertion, also limit the scope of religion. In this paper, we will reflect on the re

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47

Duverney, Daniel, and Kumiko Nishioka. "An inductive method for proving the transcendence of certain series." Acta Arithmetica 110, no. 4 (2003): 305–30. http://dx.doi.org/10.4064/aa110-4-1.

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48

Tanaka, T. A. "Transcendence of the values of certain series with Hadamard's gaps." Archiv der Mathematik 78, no. 3 (2002): 202–9. http://dx.doi.org/10.1007/s00013-002-8237-x.

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49

MCILROY, M. DOUGLAS. "Power series, power serious." Journal of Functional Programming 9, no. 3 (1999): 325–37. http://dx.doi.org/10.1017/s0956796899003299.

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50

Moyaert, Paul. "Compassionate Love: Bearing Transcendence." Tattva - Journal of Philosophy 6, no. 1 (2014): 55–72. http://dx.doi.org/10.12726/tjp.11.4.

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The view that charity consists in an expansion of existing interpersonal relations is rather misleading. We need to see it as a radical transformation, of existing relations, even if this suspension is only temporary. In charity we see a person as someone who is no longer capable of reacting appropriately. Someone who is no longer capable of behaving as a „person‟ nevertheless continues to be a person. She does not lose her personal sanctity or dignity even if she has lost a practical grasp on controlling and guiding the course of her life. Today we often tend to reduce charity to a compassion

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