Saminathan Ponnusamy

Bio: Saminathan Ponnusamy is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Unit disk & Analytic function. The author has an hindex of 34, co-authored 398 publications receiving 4446 citations. Previous affiliations of Saminathan Ponnusamy include Institute of Mathematical Sciences, Chennai & Indian Statistical Institute.

Asymptotic expansions and inequalities for hypergeometric function

Abstract: Ramanujan's work on the asymptotic behaviour of the hypergeometric function has been recently refined to the zero-balanced Gaussian hypergeometric function F(a, b; a + b; x) as x→1.We extend these results for F(a, b; c; x) when a, b, c>0 and c

Starlikeness and convexity of generalized Bessel functions

Abstract: In this paper, we give sufficient conditions for the parameters of the normalized form of the generalized Bessel functions to be convex and starlike in the open unit disk. As an application of our main results, we solve a recent open problem concerning a subordination property of Bessel functions with different parameters. Moreover, we present a new inequality for the Euler gamma function, which we apply in order to have tight bounds for the generalized and normalized Bessel function of the first kind.

Univalence and Convexity Properties for Gaussian Hypergeometric Functions

Abstract: Let A = {f : ∆ → C | f(z) = z + ∑∞ n=2 Anzn}. We study sufficient/necessary conditions, in terms of the coefficients An, for a function f ∈ A to be member of well-known subclasses of the class S of univalent functions. Examples of these subclasses include starlike, convex, close-to-convex functions. In particular, functions of the form z2F1(a, b; c; z) are considered, where 2F1(a, b; c; z) is the hypergeometric function.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Advanced Calculus I

Abstract: WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

A Course In Functional Analysis

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The Laplace Transform

Abstract: THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)

Abstract: A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.