Transformations of Ramanujan’s Summation Formula and Its Applications

نویسندگان

  • Chandrashekar Adiga
  • Taekyun Kim
چکیده

In this paper, we obtain some new transformation formulas for Ramanujan’s 1ψ1 summation formula and also establish some eta-function identities. We also deduce a q-Gamma function identity, a q-integral and some interesting series representations for π 3/2 2 √ 2Γ2(3/4) and the beta function B(x,y).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Elementary Proof of Ramanujan’s Circular Summation Formula and Its Generalizations

In this paper, we give a completely elementary proof of Ramanujan’s circular summation formula of theta functions and its generalizations given by S. H. Chan and Z. -G. Liu, who used the theory of elliptic functions. In contrast to all other proofs, our proofs are elementary. An application of this summation formula is given.

متن کامل

Curious Extensions of Ramanujan’s 1ψ1 Summation Formula

We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan’s 1ψ1 summation and a very-well-poised 4ψ6 summation as special c...

متن کامل

A NEW An EXTENSION OF RAMANUJAN'S 1 1 SUMMATION WITH APPLICATIONS TO MULTILATERAL An SERIES

Abstract. In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system An. First, we apply Ismail’s [15] argument to an An q-binomial theorem of Milne [25, Th. 5.42] and derive a new An generalization of Ramanujan’s 1ψ1 summation theorem. From this new An 1ψ1 summation and from an An 1ψ1 summation of Gustafson [9] we deduce two lemmas for...

متن کامل

Frobenius Partitions and the Combinatorics of Ramanujan's Summation

We examine the combinatorial significance of Ramanujan’s famous summation. In particular, we prove bijectively a partition theoretic identity which implies the summation formula.

متن کامل

Semi-Finite Forms of Bilateral Basic Hypergeometric Series

Abstract. We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s 1ψ1 summation, Bailey’s 2ψ2 transformations, and Bailey’s 6ψ6 summation. Corresponding Author: William Y. C. Chen, Email: [email protected] AMS Cl...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005