Yoshimoto, Ramanujan's formula and modular forms, Number Theoretic Method-Future Trends, (ed. S. Kanemitsu and C. Jia) Kluwer Acakdemic Publisher, Dordrecht (2003), 159-212.S. Kanemitsu, Y. Tanigawa, M. Yoshimoto, Ramanujan's formula and mo- dular forms, in: Number-theoretic methods-...
Hardy: "It would be difficult to find more beautiful formulae than the 'Rogers-Ramanujan' identities, but here Ramanujan must take second place to Rogers; and, if I had to select one formula from all Ramanujan's work, I would agree with Major MacMahon in selecting (1)." 准备工作:q-级...
Ramanujan’s Formula for ζ(2n + 1) Chapter © 2017 Note on two modular equations of Ramanujan Article 14 November 2022 Keywords Invariant approximation elliptic function equation function identity theta function transformation Search within this book Search Table of contents (17 chapters...
Approximating Pi by Using Ramanujan's Formula Open in MATLAB Online Hi. This is my first post so please let me know if I violate any kind of rules. Thank you in advance. I intend to approximate pi by summing a specified number of terms (k). The output I got was nowhere near what I...
Ramanujan\"s remarkable summation formula and an interesting convolution identity SBC Adiga,DD Somashekara - 《Bulletin of the Australian Mathematical Society》 被引量: 0发表: 1993年 Efficient calculation of the free-space periodic Green's function A method is discussed to overcome the slow ...
Now put τ=i/10 so that q=e−2π/10 and apply the transformation formula for the eta function (1.7) to deduce (k1+k−k2)(1−k21−4k−k2)2|q=e−2π/10=(η(5i10)η(i10))6=1125(η(2i10)η(10i10))6. (7.1) On the other hand, from (4.7) and (4.9) we have...
Ramanujans Master Theorem states that, under suitable conditions, the Mellin transform of a power series provides an interpolation formula for the coeffici... G Ólafsson,A Pasquale - 《Journal of Functional Analysis》 被引量: 16发表: 2012年 Eisenstein series and elliptic functions on [formula ...
inthetransformationformulae,numerous identitiesoftheRogers—Rmnanujantype canbeobtained.Amongthem,twohundred selectedonesaredisplayed indetails,including mostofSlater’Scollectionof130iden’ titiesandseveralnewidentities.Considering the importance ofSlater’Smonumental ...
FormulaWe employ Ramanujan's 1ψ1 formula to prove three conjectures of R. S. Melham on representation of an integer n as sums of polygonal numbers.doi:10.1155/2014/738948Bipul Kumar SarmahInternational Journal of Mathematics and Mathematical Sciences...
In this paper we generalize Ramanujan's Master Theorem to the context of a Siegel domain of Type II, which is the Hermitian symmetric space of a real non-c... H Ding - 《Ramanujan Journal》 被引量: 12发表: 1997年 CODING THE PRINCIPAL CHARACTER FORMULA FOR AFFINE KAC-MOODY LIE ALGEBRAS...