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Journal articles on the topic 'Ramanujan cubic continued fraction'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Adiga, Chandrashekar, A. Vanitha, and M. S. Surekha. "Continued Fractions of Order Six and New Eisenstein Series Identities." Journal of Numbers 2014 (May 27, 2014): 1–6. http://dx.doi.org/10.1155/2014/643241.

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We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers-Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.

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2

BARUAH, NAYANDEEP DEKA, and KANAN KUMARI OJAH. "SOME CONGRUENCES DEDUCIBLE FROM RAMANUJAN'S CUBIC CONTINUED FRACTION." International Journal of Number Theory 07, no. 05 (2011): 1331–43. http://dx.doi.org/10.1142/s1793042111004745.

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We present some interesting Ramanujan-type congruences for some partition functions arising from Ramanujan's cubic continued fraction. One of our results states that if p3(n) is defined by [Formula: see text], then p3(9n + 8) ≡ 0 (mod 34).

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3

CHAN, HEI-CHI. "RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION." International Journal of Number Theory 06, no. 04 (2010): 819–34. http://dx.doi.org/10.1142/s1793042110003241.

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4

Chan, Heng. "On Ramanujan's cubic continued fraction." Acta Arithmetica 73, no. 4 (1995): 343–55. http://dx.doi.org/10.4064/aa-73-4-343-355.

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5

Chan, Heng Huat, and Kok Ping Loo. "Ramanujan's cubic continued fraction revisited." Acta Arithmetica 126, no. 4 (2007): 305–13. http://dx.doi.org/10.4064/aa126-4-2.

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6

Berndt, Bruce, Heng Chan, and Liang-Cheng Zhang. "Ramanujan's class invariants and cubic continued fraction." Acta Arithmetica 73, no. 1 (1995): 67–85. http://dx.doi.org/10.4064/aa-73-1-67-85.

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7

Naika, M. S. Mahadeva, S. Chandankumar, and K. Sushan Bairy. "New identities for Ramanujan's cubic continued fraction." Functiones et Approximatio Commentarii Mathematici 46, no. 1 (2012): 29–44. http://dx.doi.org/10.7169/facm/2012.46.1.3.

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8

Deka Baruah, Nayandeep. "Modular Equations for Ramanujan's Cubic Continued Fraction." Journal of Mathematical Analysis and Applications 268, no. 1 (2002): 244–55. http://dx.doi.org/10.1006/jmaa.2001.7823.

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9

CHAN, HEI-CHI. "RAMANUJAN'S CUBIC CONTINUED FRACTION AND AN ANALOG OF HIS "MOST BEAUTIFUL IDENTITY"." International Journal of Number Theory 06, no. 03 (2010): 673–80. http://dx.doi.org/10.1142/s1793042110003150.

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10

Cho, Bumkyu, Ja Kyung Koo, and Yoon Kyung Park. "On Ramanujan's cubic continued fraction as a modular function." Tohoku Mathematical Journal 62, no. 4 (2010): 579–603. http://dx.doi.org/10.2748/tmj/1294170348.

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11

Kumar, B. R. Srivatsa, and T. G. Sreeramamurthy. "Two identities of Ramanujan's cubic continued fraction by modular equations." International Journal of Contemporary Mathematical Sciences 8 (2013): 271–80. http://dx.doi.org/10.12988/ijcms.2013.13029.

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12

Naika, Megadahalli Sidda Naika Mahadeva, Mugur Chinna Swamy Maheshkumar, and Kurady Sushan Bairy. "General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction." Kyungpook mathematical journal 49, no. 3 (2009): 435–50. http://dx.doi.org/10.5666/kmj.2009.49.3.435.

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13

Chan, Hei-Chi. "A new proof of two identities involving Ramanujan’s cubic continued fraction." Ramanujan Journal 21, no. 2 (2009): 173–80. http://dx.doi.org/10.1007/s11139-009-9203-z.

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14

Baruah, Nayandeep Deka, and Nipen Saikia. "Some general theorems on the explicit evaluations of Ramanujan's cubic continued fraction." Journal of Computational and Applied Mathematics 160, no. 1-2 (2003): 37–51. http://dx.doi.org/10.1016/s0377-0427(03)00612-5.

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15

Yao, Olivia X. M. "Infinite families of congruences modulo 5 and 7 for the cubic partition function." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 5 (2019): 1189–205. http://dx.doi.org/10.1017/prm.2018.61.

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AbstractIn 2010, Hei-Chi Chan introduced the cubic partition function a(n) in connection with Ramanujan's cubic continued fraction. Chen and Lin, and Ahmed, Baruah and Dastidar proved that a(25n + 22) ≡ 0 (mod 5) for n ⩾ 0. In this paper, we prove several infinite families of congruences modulo 5 and 7 for a(n). Our results generalize the congruence a(25n + 22) ≡ 0 (mod 5) and four congruences modulo 7 for a(n) due to Chen and Lin. Moreover, we present some non-standard congruences modulo 5 for a(n) by using an identity of Newman. For example, we prove that $a((({15\times 17^{3\alpha }+1})/{8}

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16

Jain, Rama. "An introduction to Ramanujan’s continued fractions." Anusandhaan - Vigyaan Shodh Patrika 3, no. 01 (2015): 77–82. https://doi.org/10.22445/avsp.v3i01.8580.

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Continued fraction is a method of writing a fraction in a different way. The Rogers-Ramanujan continued fraction is defined as R(q)= ____q1/5_____________ ,|q| less than1 1+ ____q_________ 1+ ____q2________ 1+ ____q3___ 1+……. In his first two letters of G.H.Hardy, and his note book, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fractions. In the year 2000, Bruce C. Provided proof for many of claims about the Roger-Ramanujan and generalized Rogers-Ramanujan continued fractions . found in the lost note book. These fractions are also related to Jigsaw Puzzle problems of di

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17

BOWMAN, D., J. Mc LAUGHLIN, and N. J. WYSHINSKI. "A q-CONTINUED FRACTION." International Journal of Number Theory 02, no. 04 (2006): 523–47. http://dx.doi.org/10.1142/s179304210600070x.

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We use the method of generating functions to find the limit of a q-continued fraction, with 4 parameters, as a ratio of certain q-series. We then use this result to give new proofs of several known continued fraction identities, including Ramanujan's continued fraction expansions for (q2; q3)∞/(q; q3)∞and [Formula: see text]. In addition, we give a new proof of the famous Rogers–Ramanujan identities. We also use our main result to derive two generalizations of another continued fraction due to Ramanujan.

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18

Berndt, Bruce C., Heng Huat Chan, Sen-Shan Huang, Soon-Yi Kang, Jaebum Sohn, and Seung Hwan Son. "The Rogers–Ramanujan continued fraction." Journal of Computational and Applied Mathematics 105, no. 1-2 (1999): 9–24. http://dx.doi.org/10.1016/s0377-0427(99)00033-3.

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19

Adiga, C., and N. Anitha. "A note on a continued fraction of Ramanujan." Bulletin of the Australian Mathematical Society 70, no. 3 (2004): 489–97. http://dx.doi.org/10.1017/s0004972700034742.

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Ramanujan recorded many beautiful continued fractions in his notebooks. In this paper, we derive several indentities involving the Ramanujan continued fraction c(q), including relations between c(q) and c(qn). We also obtain explicit evaluations of for various positive integers n.

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20

Bernd, Bruce C., and Heng Huat Chan. "Some Values for the Rogers-Ramanujan Continued Fraction." Canadian Journal of Mathematics 47, no. 5 (1995): 897–914. http://dx.doi.org/10.4153/cjm-1995-046-5.

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AbstractIn his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have been proved by K. G. Ramanathan, using mostly ideas with which Ramanujan was unfamiliar. In this paper, eight of Ramanujan's values are established; four are proved for the first time, while the remaining four had been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identities, which have not been heretofore used for evaluating continued fractions.

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21

Adiga, Chandrashekar, Saeed Bulkhali, Yilmaz Simsek, and H. M. Srivastava. "A continued fraction of Ramanujan and some Ramanujan-Weber class invariants." Filomat 31, no. 13 (2017): 3975–97. http://dx.doi.org/10.2298/fil1713975a.

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22

Buslaev, V. I. "Convergence of the Rogers-Ramanujan continued fraction." Sbornik: Mathematics 194, no. 6 (2003): 833–56. http://dx.doi.org/10.1070/sm2003v194n06abeh000741.

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23

Lee, Yoonjin, and Yoon Kyung Park. "Modularity of a Ramanujan–Selberg continued fraction." Journal of Mathematical Analysis and Applications 438, no. 1 (2016): 373–94. http://dx.doi.org/10.1016/j.jmaa.2016.01.065.

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24

Bagis, Nikos, and M. Lawrence Glasser. "Evaluations of a continued fraction of Ramanujan." Rendiconti del Seminario Matematico della Università di Padova 133 (2015): 1–10. http://dx.doi.org/10.4171/rsmup/133-1.

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25

Buslaev, V. I., and S. F. Buslaeva. "On the Rogers--Ramanujan Periodic Continued Fraction." Mathematical Notes 74, no. 5/6 (2003): 783–93. http://dx.doi.org/10.1023/b:matn.0000009014.24386.11.

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26

Achuthan, P., and S. Ponnuswamy. "Padé approximants and Eisenstein— Ramanujan continued fraction." Journal of Computational and Applied Mathematics 41, no. 3 (1992): 247–64. http://dx.doi.org/10.1016/0377-0427(92)90134-j.

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27

Baruah, Nayandeep Deka, and P. Bhattacharyya. "Some theorems on the explicit evaluation of Ramanujan's theta-functions." International Journal of Mathematics and Mathematical Sciences 2004, no. 40 (2004): 2149–59. http://dx.doi.org/10.1155/s0161171204111058.

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Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants.

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28

Rana, M., and H. Kaur. "SOME MATCHING COEFFICIENTS OF q−PRODUCTS." South East Asian J. of Mathematics and Mathematical Sciences 20, no. 01 (2024): 405–24. http://dx.doi.org/10.56827/seajmms.2024.2001.31.

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We find some results on matching coefficients for certain q-products. Some of the results are associated with Rogers−Ramanujan continued fraction R(q) = (q, q4; q5)∞ (q2, q3; q5)∞ , while some are associated with analogous of Rogers−Ramanujan functions. The techniques used for proving the results involves Ramanujan’s theta functions, identities for Rogers−Ramanujan type functions, and q-series manipulations.

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29

Shiokawa, Iekata. "Rational approximations to the Rogers-Ramanujan continued fraction." Acta Arithmetica 50, no. 1 (1988): 23–30. http://dx.doi.org/10.4064/aa-50-1-23-30.

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30

Bagis, Nikos. "Parametric Evaluations of the Rogers-Ramanujan Continued Fraction." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/940839.

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31

Zhang, Liang-Cheng. "Explicit evaluations of a Ramanujan-Selberg continued fraction." Proceedings of the American Mathematical Society 130, no. 1 (2001): 9–14. http://dx.doi.org/10.1090/s0002-9939-01-06183-4.

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32

Cho, Bumkyu, Ja Kyung Koo, and Yoon Kyung Park. "Arithmetic of the Ramanujan–Göllnitz–Gordon continued fraction." Journal of Number Theory 129, no. 4 (2009): 922–47. http://dx.doi.org/10.1016/j.jnt.2008.09.018.

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33

Vasuki, K. R., and B. R. Srivatsa Kumar. "Certain identities for Ramanujan–Göllnitz–Gordon continued fraction." Journal of Computational and Applied Mathematics 187, no. 1 (2006): 87–95. http://dx.doi.org/10.1016/j.cam.2005.03.038.

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34

Alladi, Krishnaswami, and Basil Gordon. "Partition identities and a continued fraction of Ramanujan." Journal of Combinatorial Theory, Series A 63, no. 2 (1993): 275–300. http://dx.doi.org/10.1016/0097-3165(93)90061-c.

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35

Deka Baruah, Nayandeep, and Nipen Saikia. "Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction." Monatshefte für Mathematik 154, no. 4 (2008): 271–88. http://dx.doi.org/10.1007/s00605-007-0515-z.

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36

Dharmendra, B. N., M. R. Rajesh Kanna, and H. L. Parashivamurthy. "Some new modular identities of Ramanujan continued fraction." International Journal of Contemporary Mathematical Sciences 8 (2013): 249–55. http://dx.doi.org/10.12988/ijcms.2013.13026.

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37

Gee, Alice, and Mascha Honsbeek. "Singular values of the Rogers-Ramanujan continued fraction." Ramanujan Journal 11, no. 3 (2006): 267–84. http://dx.doi.org/10.1007/s11139-006-8477-7.

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38

Borwein, Jonathan M., and D. Russell Luke. "Dynamics of a continued fraction of Ramanujan with random coefficients." Abstract and Applied Analysis 2005, no. 5 (2005): 449–67. http://dx.doi.org/10.1155/aaa.2005.449.

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We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.

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39

ANTONIOU, GEORGE E., and PANAGIOTA A. KATSALIS. "ON THE 1D AND 2D ROGERS–RAMANUJAN CONTINUED FRACTIONS." Journal of Circuits, Systems and Computers 20, no. 04 (2011): 573–85. http://dx.doi.org/10.1142/s0218126611007475.

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In this paper the classical and generalized numerical Rogers–Ramanujan continued fractions are extended to a polynomial continued fraction in one and two dimensions. Using the new continued fractions, the fundamental recurrence formulas and a fast algorithm, based on matrix formulations, are given for the computation of their transfer functions. The presented matrix formulations can provide a new perspective to the analysis and design of Ladder-continued fraction filters in one and two dimensions signal processing. The simplicity and efficiency of the presented algorithms are illustrated by st

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40

Rawat, Pramod Kumar. "On Generalized Mock Theta Functions of Tenth Order." Trends in Sciences 19, no. 3 (2022): 2070. http://dx.doi.org/10.48048/tis.2022.2070.

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In this paper we have given 3 independent variable generalization of tenth order mock theta functions and have found some relations between generalized mock theta functions of different order. We have given a continued fraction representation of generalized tenth order mock theta functions. We have also given the q-integral representation and multibasic expansion for these functions. Further by specializing the parameters we have connected mock theta functions with continued fraction of Ramanujan. HIGHLIGHTS  Mock theta functions are last gift to mathematics by Ramanujan. The

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41

Saikia, Nipen. "Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/694251.

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42

Masson, David R. "Some Continued Fractions of Ramanujan and Meixner-Pollaczek Polynomials." Canadian Mathematical Bulletin 32, no. 2 (1989): 177–81. http://dx.doi.org/10.4153/cmb-1989-026-1.

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43

M.P. Chaudhary. "Generalization for character formulas in terms of continued fraction identities." Malaya Journal of Matematik 2, no. 01 (2014): 24–34. http://dx.doi.org/10.26637/mjm201/004.

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In recent work, Folsom discussed character formulas for classical mock theta functions of Ramanujan. Here, we suggest representations for character formulas in terms of continued fraction identities or in more precise language, we can say an applications of continued fraction identities to character formulas. As a consequence, we obtain fourteen new results.

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44

Srivastava, Bhaskar. "On the coefficients of a continued fraction of Ramanujan." Publications de l'Institut Math?matique (Belgrade) 111, no. 125 (2022): 123–26. http://dx.doi.org/10.2298/pim2225123s.

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45

Andrews, George E., and Douglas Bowman. "A full extension of the Rogers-Ramanujan continued fraction." Proceedings of the American Mathematical Society 123, no. 11 (1995): 3343. http://dx.doi.org/10.1090/s0002-9939-1995-1277090-8.

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46

Srivastava, Bhaskar. "SOME IDENTITIES CONNECTED WITH A CONTINUED FRACTION OF RAMANUJAN." Taiwanese Journal of Mathematics 16, no. 3 (2012): 829–38. http://dx.doi.org/10.11650/twjm/1500406659.

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47

Yuttanan, Boonrod. "New properties for the Ramanujan–Göllnitz–Gordon continued fraction." Acta Arithmetica 151, no. 3 (2012): 293–310. http://dx.doi.org/10.4064/aa151-3-5.

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48

Saikia, Nipen, and Chayanika Boruah. "Some new explicit values of Ramanujan–Selberg continued fraction." Afrika Matematika 28, no. 7-8 (2017): 1131–41. http://dx.doi.org/10.1007/s13370-017-0507-7.

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49

Wegert, Elias. "About the Cover: The Continued Fraction of Rogers–Ramanujan." Computational Methods and Function Theory 19, no. 1 (2019): 1–2. http://dx.doi.org/10.1007/s40315-019-00261-4.

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50

Saikia, Nipen. "Some new identities for a continued fraction of Ramanujan." ANNALI DELL'UNIVERSITA' DI FERRARA 62, no. 1 (2016): 151–64. http://dx.doi.org/10.1007/s11565-016-0239-x.

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