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Готові списки джерел за темами / Sum of the series / Статті в журналах

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Статті в журналах з теми "Sum of the series"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

Kraines, David P., Vivian Y. Kraines, and David A. Smith. "Sum the Alternating Harmonic Series." College Mathematics Journal 20, no. 5 (1989): 433. http://dx.doi.org/10.2307/2686934.

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2

de Bruijn, N. G., and Rolf Richberg. "Sum of a Series: 11131." American Mathematical Monthly 113, no. 7 (2006): 661. http://dx.doi.org/10.2307/27642024.

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3

Sahadat Sarkar, Najmuj. "The Sum of Fibionacci Series." International Journal of Mathematics and Statistics Invention 13, no. 2 (2025): 01–03. https://doi.org/10.35629/4767-13020103.

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4

Laszlo, Akos. "The Sum of Some Convergent Series." American Mathematical Monthly 108, no. 9 (2001): 851. http://dx.doi.org/10.2307/2695557.

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5

Ramirez, Oscar Ciaurri, and Daniele Donini. "Sum of an Infinite Series: 10867." American Mathematical Monthly 109, no. 6 (2002): 575. http://dx.doi.org/10.2307/2695460.

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6

Kalman, Dan. "Six Ways to Sum a Series." College Mathematics Journal 24, no. 5 (1993): 402. http://dx.doi.org/10.2307/2687013.

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7

Fomin, V. I. "About One Designation of Series Sum." Voprosy sovremennoj nauki i praktiki. Universitet imeni V.I. Vernadskogo, no. 2(64) (2017): 157–59. http://dx.doi.org/10.17277/voprosy.2017.02.pp.157-159.

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8

Harper, James D. "Estimating the Sum of Alternating Series." College Mathematics Journal 19, no. 2 (1988): 149. http://dx.doi.org/10.2307/2686176.

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9

Kholshchevnikova, N. N. "Sum of Everywhere Convergent Trigonometric Series." Mathematical Notes 75, no. 3/4 (2004): 439–43. http://dx.doi.org/10.1023/b:matn.0000023326.92961.ce.

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10

Harper, James D. "Estimating the Sum of Alternating Series." College Mathematics Journal 19, no. 2 (1988): 149–53. http://dx.doi.org/10.1080/07468342.1988.11973103.

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11

Gorfin, Alan. "Evaluating the Sum of the Series." College Mathematics Journal 20, no. 4 (1989): 329–31. http://dx.doi.org/10.1080/07468342.1989.11973254.

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12

Kalman, Dan. "Six Ways to Sum a Series." College Mathematics Journal 24, no. 5 (1993): 402–21. http://dx.doi.org/10.1080/07468342.1993.11973562.

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13

Chelidze, G., G. Giorgobiani, and V. Tarieladze. "Sum Range of a Quaternion Series." Journal of Mathematical Sciences 216, no. 4 (2016): 519–21. http://dx.doi.org/10.1007/s10958-016-2908-9.

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14

László, Ákos. "The Sum of Some Convergent Series." American Mathematical Monthly 108, no. 9 (2001): 851–55. http://dx.doi.org/10.1080/00029890.2001.11919819.

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15

Kadets, V. M. "Sum regions of weakly convergent series." Functional Analysis and Its Applications 23, no. 2 (1989): 133–35. http://dx.doi.org/10.1007/bf01078784.

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16

Plaza, Ágnel. "Proof without words: partial sum and sum of a geometric series." Teaching Mathematics and Computer Science 2, no. 2 (2015): 423. http://dx.doi.org/10.5485/tmcs.2004.0075.

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17

Tetunashvili, Sh. "Functional series representable as a sum of two universal series." Doklady Mathematics 96, no. 3 (2017): 578–79. http://dx.doi.org/10.1134/s106456241706014x.

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18

Ash, Kute. "Ramanujan Sum of All Natural Numbers without Grandi Series." International Journal of Science and Research (IJSR) 13, no. 4 (2024): 1326–27. http://dx.doi.org/10.21275/sr24321135426.

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19

Virtanen, Jouko J. "85.05 Using Intuition to Sum a Series." Mathematical Gazette 85, no. 502 (2001): 86. http://dx.doi.org/10.2307/3620477.

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20

Abramov, Vyachslav. "Evaluating the sum of convergent positive series." Publications de l'Institut Math?matique (Belgrade) 111, no. 125 (2022): 41–53. http://dx.doi.org/10.2298/pim2225041a.

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Анотація:

We provide numerical procedures for possibly best evaluating the sum of positive series under quite general setting. Our procedures are based on the application of a generalized version of Kummer's test.

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21

Paudyal, Daya Ram, and Lakshmi Narayan Mishra. "ON APPROXIMATION OF SUM OF CONVERGENT SERIES." Journal of Engineering and Exact Sciences 6, no. 3 (2020): 0421–28. http://dx.doi.org/10.18540/jcecvl6iss3pp0421-0428.

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Анотація:

The paper has given a clear opinion on the progress of environmental protection and sustainability in the Nigerian context. The environmental regulations scenario in the country is marred by malpractices and corruption more stringent policy enforcement will help in the achievement of environmental protection. This paper deals with a specialized method of approximating the sum of an infinite series containing positive terms which are monotonically decreasing. The analysis has been done by taking some references done by the great mathematician Leonhard Euler with some special examples. Consequen

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22

白, 颖. "Convergence and Sum Function of Power Series." Advances in Applied Mathematics 09, no. 08 (2020): 1221–29. http://dx.doi.org/10.12677/aam.2020.98143.

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23

Carlson, G. T., and B. L. Illman. "Series capacitors and the inverse sum rule." American Journal of Physics 70, no. 11 (2002): 1122–28. http://dx.doi.org/10.1119/1.1506170.

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24

Chan, Song Heng, and Byungchan Kim. "On some double-sum false theta series." Journal of Number Theory 190 (September 2018): 40–55. http://dx.doi.org/10.1016/j.jnt.2018.02.012.

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25

Igarashi, Masahiro. "Cyclic sum of certain parametrized multiple series." Journal of Number Theory 131, no. 3 (2011): 508–18. http://dx.doi.org/10.1016/j.jnt.2010.09.011.

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26

Wituła, Roman, and Damian Słota. "On the sum of some alternating series." Computers & Mathematics with Applications 62, no. 6 (2011): 2658–64. http://dx.doi.org/10.1016/j.camwa.2011.08.008.

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27

Sheremeta, Myroslav Mykolayovych, Yulia Vasylivna Stets, and Oksana Markiyanivna Sumyk. "Estimates of a sum of Dirichlet series." Journal of Mathematical Sciences 194, no. 5 (2013): 557–72. http://dx.doi.org/10.1007/s10958-013-1546-8.

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28

Scott, J. A. "98.12 A convergent series with zero sum." Mathematical Gazette 98, no. 542 (2014): 325–27. http://dx.doi.org/10.1017/s0025557200001388.

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29

Reynolds, Robert, and Allan Stauffer. "Extended de Montmort-Prudnikov Sum." Mathematics 11, no. 2 (2023): 333. http://dx.doi.org/10.3390/math11020333.

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Анотація:

Using a contour integral method, the de Montmort-Prudnikov sum is extended to derive a new series representation involving the incomplete gamma function. The series is uniformly convergent and completely analytical, which can be evaluated for general complex ranges of the parameters involved. Applications and evaluations of this formula are discussed.

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30

Stojiljkovic, Vuk. "Series involving Dirichlet Eta function." Gulf Journal of Mathematics 15, no. 1 (2023): 67–83. http://dx.doi.org/10.56947/gjom.v15i1.1135.

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Анотація:

In this article, we obtain an integral representation for a remainder sum of the Dirichlet Eta function. We then obtain numerous generating functions and series concerning the usage of the obtained integral representation. Alternating Fibonacci sum of the partial sum of the Dirichlet Eta function has been obtained, as well as the squared version Fibonacci series concerning the sum. A generalized representation of the product of polynomials concerning the partial sum of the Dirichlet Eta function has been obtained. Numerous examples have been provided to showcase the derived results.

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31

Patel, Gaurav Singh, and Saurabh Kumar Gautam. "Ramanujan: The New Sum of All Natural Numbers." International Journal for Research in Applied Science and Engineering Technology 10, no. 2 (2022): 1272–74. http://dx.doi.org/10.22214/ijraset.2022.40511.

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Анотація:

Abstract: As we know that Sir Ramanujan gave the solution of sum of all natural numbers up to infinity and said that the sum of all natural numbers till infinity is -1/12. I studied on this topic and found that if we try to solve the infinite series in a slightly different way, then we get the answer of its sum different from -1/12, so this is what I have written in this paper that such Ramanujan Sir, what was the mistake in solving the infinite series, which by solving it in a slightly different way from the same concept, we get different answers. Keywords: Ramanujan the new sum of all natura

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32

NASH-WILLIAMS, C. St J. A., and D. J. WHITE. "Rearrangement of vector series. II." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 111–34. http://dx.doi.org/10.1017/s0305004100004825.

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Let [sum ]∞an denote the set of cluster points of the sequence of partial sums of a series [sum ]an with terms in ℝd. For any permutation f of the set ℕ of positive integers, [Cscr ]f (ℝd) denotes the set of all sets [sum ]∞af(n) arising from series [sum ]an with terms in ℝd and sum 0. For each f, we use the Max-Flow Min-Cut Theorem to determine all convex sets in [Cscr ]f(ℝd) which are symmetric about a point. These sets depend only on a parameter w(f) ∈ ℕ ∪ {0, ∞}, called the width of f. We show that w(f), when it is a positive integer, falls far short of completely determining [Cscr ]f(ℝd)

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33

S, Sriram, and David Christopher A. "Raising Series to A Power." Indian Journal of Science and Technology 17, SP1 (2024): 124–35. https://doi.org/10.17485/IJST/v17sp1.249.

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Анотація:

Abstract <strong>Objective.</strong> Let be a formal power series and let . In this note, we consider the function . We find that if has a series expansion at , then its coefficients are polynomials in . The coefficients of these polynomials were found to be a weighted composition sum. <strong>Methods.</strong> The method to arrive at this representation involves logarithmic derivative and exponential representation. <strong>Findings.</strong> As a consequence of this, new identities involving partition functions and binomial coefficients were obtained. Further, a part

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34

Rungratgasame, Thitarie, and Punna Charrasangsakul. "Partial-Sum Matrix and its Rank." WSEAS TRANSACTIONS ON MATHEMATICS 22 (October 20, 2023): 768–72. http://dx.doi.org/10.37394/23206.2023.22.84.

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Анотація:

A partial-sum matrix is a matrix whose entries are partial sums of a seires associate with a sequence. The rank of a partial-sum matrix associate with any recurrence sequence can be related to the rank of an associate recurrence matrix, a matrix whose entries are from the same recurrence sequence. In particular, we find ranks of partial-sum matrices associated with arithmetic series and geometric series.

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35

Sriram, S., and A. David Christopher. "Raising Series to A Power." Indian Journal Of Science And Technology 17, SPI1 (2024): 124–35. http://dx.doi.org/10.17485/ijst/v17sp1.249.

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Анотація:

Objective. Let be a formal power series and let . In this note, we consider the function . We find that if has a series expansion at , then its coefficients are polynomials in . The coefficients of these polynomials were found to be a weighted composition sum. Methods. The method to arrive at this representation involves logarithmic derivative and exponential representation. Findings. As a consequence of this, new identities involving partition functions and binomial coefficients were obtained. Further, a particular class of Dirichlet series is found to have the form of an exponential function

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36

Rudin, Walter. "Power series with zero-sum on countable sets." Complex Variables, Theory and Application: An International Journal 18, no. 3-4 (1992): 283–84. http://dx.doi.org/10.1080/17476939208814553.

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37

Lin, De-Hone. "Path integral solution by sum over perturbation series." Journal of Mathematical Physics 41, no. 5 (2000): 2723–31. http://dx.doi.org/10.1063/1.533266.

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38

Unal, Hasan. "Proof Without Words: Sum of an Infinite Series." College Mathematics Journal 40, no. 1 (2009): 39. http://dx.doi.org/10.1080/07468342.2009.11922334.

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39

An, Yajun, and Tom Edgar. "“Sum” Visual Rearrangements of the Alternating Harmonic Series." College Mathematics Journal 50, no. 4 (2019): 280–85. http://dx.doi.org/10.1080/07468342.2019.1655375.

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40

Li, Zhonghua, and Ende Pan. "Sum of interpolated finite multiple harmonic q-series." Journal of Number Theory 201 (August 2019): 148–75. http://dx.doi.org/10.1016/j.jnt.2019.02.024.

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41

Greene, J., and D. Stanton. "A character sum evaluation and Gaussian hypergeometric series." Journal of Number Theory 23, no. 1 (1986): 136–48. http://dx.doi.org/10.1016/0022-314x(86)90009-0.

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42

Krivosheev, Aleksandr Sergeevich, and Olesya Aleksandrovna Krivosheeva. "A closedness of set of Dirichlet series sum." Ufimskii Matematicheskii Zhurnal 5, no. 3 (2013): 94–117. http://dx.doi.org/10.13108/2013-5-3-94.

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43

Unal, Hasan. "Proof Without Words: Sum of an Infinite Series." College Mathematics Journal 40, no. 1 (2009): 39. http://dx.doi.org/10.4169/193113409x469695.

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44

Jaraldpushparaj, S., and G. Britto Antony Xavier. "Extended Mittag-Leffler function, series and its sum." Journal of Physics: Conference Series 1597 (July 2020): 012005. http://dx.doi.org/10.1088/1742-6596/1597/1/012005.

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45

Shen, Lu-Ming, and Jun Wu. "On the error-sum function of Lüroth series." Journal of Mathematical Analysis and Applications 329, no. 2 (2007): 1440–45. http://dx.doi.org/10.1016/j.jmaa.2006.07.049.

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46

Makarov, V. Yu. "Characteristics of the sum of a multidimensional series." Ukrainian Mathematical Journal 46, no. 7 (1994): 971–78. http://dx.doi.org/10.1007/bf01056674.

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47

Sangarsu, Raghaven Rao. "Ramanujan Sums of All Natural Numbers with Grandi Series." Journal of Research in Vocational Education 6, no. 9 (2024): 3–4. http://dx.doi.org/10.53469/jrve.2024.6(09).02.

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Анотація:

We are all know that the Ramanujan’s theory of calculating the sum of all the natural number. When we came to known that sum of all-natural number is ,that time everyone thinks about two things, one is how it possible that sum of positive number is negative & other is how it is very close to zero. Another research paper gives value of all natural number is then I started the study of this sum, then I find it is as zero. Quit interestingly but this value has more important than Ramanujan’s sum because I did not consider the Grandi series for calculating this sum. And then it is very easy to

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48

Chen, Chang-Pao. "L1-convergence of Fourier series." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (1986): 376–90. http://dx.doi.org/10.1017/s144678870003384x.

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Анотація:

AbstractFor an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.

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49

Nurcombe, J. R. "Alteration in the sum of alternating series by simple rearrangement." Mathematical Gazette 97, no. 539 (2013): 193–97. http://dx.doi.org/10.1017/s0025557200005763.

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Анотація:

It is well known that the sum of an absolutely convergent series is invariant under rearrangement of its terms. On the other hand, a conditionally convergent series, that is one which converges but the sum of whose absolute values is unbounded, can be rearranged to have any sum whatsoever, or diverge in any desired manner (see for example [1, §44]). A simple examplS of a conditionally convergent series is the alternating harmonic series (AHS), . In [2], the following theorem on rearrangement of the AHS was proved:Theorem A: The AHS remains convergent under a simple rearrangement (i.e. the sub-

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50

NASH-WILLIAMS, C. St J. A., and D. J. WHITE. "Rearrangement of vector series. I." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 89–109. http://dx.doi.org/10.1017/s0305004100004813.

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Анотація:

Let ℝd* = ℝd ∪ {[midast ]} be the one-point compactification of Euclidean space ℝd and d [ges ] 2. Given a permutation f of the set ℕ of positive integers, let [Cscr ]f(ℝd*) denote the set of all sets C ⊆ ℝd* for which there is a series [sum ]an in ℝd with zero sum such that C is the cluster set in ℝd* of the sequence of partial sums of [sum ]af(n). Every C ∈ [Cscr ]f(ℝd*) is non-empty, connected and closed in ℝd*. We give a combinatorial characterization of the permutations f for which all non-empty closed connected subsets of ℝd* belong to [Cscr ]f(ℝd*). For every permutation f of ℕ, we dete

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