The Journal of the Indian Mathematical Society

M. Bhimasena Rao , M. Venkatarama Ayyar

Abstract

This paper deals with the evaluation of certain infinite series and products. A few of them have already been evaluated by Dr. Glaishei and others; but, their mode of evaluation is complex, involving a knowledge of elliptic functions and modular equations. The method adopted here is fairly elementary, consisting of simple transformations of two well-known infinite integrals and is believed to be new.

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M. Bhimasena Rao , M. Venkatarama Ayyar

Abstract

In Part I of this paper several general results were obtained wherein a was put equal to πr (cos θ + i sin θ) and real and imaginary parts were separated. The equated real parts led to the evaluation of several theta-products and a few series.

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M. Venkatarama Ayyar

Abstract

In the paper on "Some Infinite Products and Series" which appeared in the J.I.M.S. (Vol. XV, Nos. 7, 10 and 11), certain results relating to 'Theta-Products' and 'inverse Tangent Series' of the type Σ₁ - Σ₂ have been established by Mr. Bhimasena Rao and myself. In this paper, I propose to evaluate, by a direct application of a few modular equations, some fresh Theta-Products and also to discuss the sums of the series Σ₁ and Σ₂ a separately.

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M. Venkatarama Ayyar ¹, M. Bhimasena Rao ¹

Affiliations
1 Bangalore, IN

Abstract

Our object in this paper is to show the underlying unity in all the six examples of Ramanujan, reducing them and his algebraic identity to one type and to extend the work to several more types.

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