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@article{JSFU_2023_16_4_a7, author = {Prathima Jayarama and Arjun Kumar Rathie}, title = {On a note on {Ap\'ery-like} series with an application}, journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika}, pages = {498--505}, publisher = {mathdoc}, volume = {16}, number = {4}, year = {2023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a7/} }
TY - JOUR AU - Prathima Jayarama AU - Arjun Kumar Rathie TI - On a note on Ap\'ery-like series with an application JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2023 SP - 498 EP - 505 VL - 16 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a7/ LA - en ID - JSFU_2023_16_4_a7 ER -
%0 Journal Article %A Prathima Jayarama %A Arjun Kumar Rathie %T On a note on Ap\'ery-like series with an application %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2023 %P 498-505 %V 16 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a7/ %G en %F JSFU_2023_16_4_a7
Prathima Jayarama; Arjun Kumar Rathie. On a note on Ap\'ery-like series with an application. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 498-505. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a7/
[1] R.Apéry, “Irrationalité de $\zeta(2)$ et $\zeta(3)$”, Journees arithmétiques de Luminy, Astérique, 61, 1979, 11–13 | MR | Zbl
[2] B.C.Berndt, P.T.Joshi, Ramanujan's Second Notebook, Chapter 9, Contemporary Mathematics, 23, American Mathematical Society, Rhode Island, 1983 | DOI | MR | Zbl
[3] J.Borwein, D.Broadhurst, J.Kamnitzer, Central binomial sums and multiple Claussen values (with connections to Zeta values), 1970
[4] R.L.Graham, D.E.Knuth, O.Patashnik, Concrete Mathematics, Second Edition, Addison-Wesley Publishing Company Inc., 1994, 262–263 | MR
[5] Y.S.Kim, M.A.Rakha, A.K.Rathie, “Extensions of certain classical summation theorems for the series $_{2} F_{1}$, $_{3} F_{2}$ and $_{4} F_{3}$ with applications in Ramanujan's summations”, Int. J. Math. Math. Sci., 2010 (2010), 309503 | MR | Zbl
[6] J.L.Lavoie, F.Grondin, A.K.Rathie, “Generalizations of Watson's theorem on the sum of a $_{3}F_{2}$”, Indian J. Math., 34:1 (1992), 23–32 | MR | Zbl
[7] J.L.Lavoie, F.Grondin, A.K. Rathie, K.Arora, “Generalizations of Dixon's theorem on the sum of a $_{3}F_{2}$”, Math. Comp., 62 (1994), 267–276 | MR | Zbl
[8] J.L.Lavoie, F.Grondin, A.K.Rathie, “Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$”, J. Comput. Appl. Math., 72 (1996), 293–300 | DOI | MR | Zbl
[9] D.H.Lehmer, “Interesting series involving the central binomial coefficient”, Amer. Math. Mon., 89:7 (1985), 449–457 | DOI | MR
[10] D.Leschiner, “Some new identities for $\zeta(k)$”, J. Number Theory, 13 (1981), 355–362 | DOI | MR
[11] A. van der Poorten, “Some wonderful formulae$\dots$ footnotes to Apéry's proof of the irrationality of $\zeta(3)$”, Sem. Delange-Pisot-Poitou, 20:2 (1978-1979), 1–7 | MR
[12] E.D.Rainville, Special Functions, The Macmillan Company, New York, 1960 | MR | Zbl
[13] M.A.Rakha, A.K.Rathie, “Generalizations of classical summation theorems for the series $_{2} F_{1}$ and $_{3} F_{2}$ with applications”, Integral Transforms Spec. Funct., 22:11 (2011), 823–840 | DOI | MR | Zbl
[14] L.J.Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, UK, 1966 | MR | Zbl
[15] T.Sherman, Summations of Glaisher and Apéry-like numbers, 2000 http://math.arizona.edu/ura/001/sherman.travis/series.pdf
[16] I.J.Zucker, “On the series $ \sum\limits_{k=1}^{\infty}\binom{2k}{k}^{-1}k^{-n}$ and related sums”, J. Number Theory, 20 (1985), 92–102 | DOI | MR | Zbl