Yoshimoto, Ramanujan's formula and modular forms, in Number-theoretic methods -- future trends (ed. by Shigeru Kanemitsu and Chaohua Jia), Kluwer Academic Publ., 2002, pp. 159-212. MR1974140 (2004g:11036)S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto, Ramanujan's formula and modular forms...
Ramanujan's Formula for $\\zeta(2n+1) In particular, we discuss the history of Ramanujan's formula, its connection to modular forms, as well as the remarkable properties of the associated polynomials. We also indicate analogues, generalizations and opportunities for further ... BC Berndt,A Str...
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...
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...
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 Development of Elliptic Functions According to Ramanujan Ramanujan's Summation FormulaQuintuple Product IdentityThis unique...
By the formulas in Theorem 1.2, we can compute each term of the sequences theoretically without using the recurrence formula. The outline of the paper is as follows. In Sect. 2, we reformulate the proof in [6] on the existence of the sequence satisfying (1.2). This section concludes with...
A simple proof of Ramanujan's summation of the 1 ψ 1 A simple proof by functional equations is given for Ramanujan's 1 ψ 1 sum. Ramanujan's sum is a useful extension of Jacobi's triple product formula, an... GE Andrews,R Askey - 《Aequationes Mathematicae》 被引量: 101发表: 1978...
Zhu, G., Wan, D.: An asymptotic formula for counting subset sums over subgroups of finite fields. Finite Fields Appl. 18, 192–209 (2012) Article MathSciNet Google Scholar Zhu, G., Wan, D.: Computing the error distance of Reed–Solomon codes. In: Agrawal, M., Cooper, S.B., Li...
In this article, we give new proofs of two of Ramanujan's $1/\unicode[STIX]{x1D70B}$ formulae $$\begin{eqnarray}\frac{1}{\unicode[STIX]{x1D70B}}=\frac{2\sqrt{2}}{99^{2}}\mathop{\sum }_{m=0}^{\infty }(26390m+1103)\frac{(4m)!}{396^{4m}(m!)^{4}}\end{eqnarray}$...