Informatics Publishing Limited

N. G. Shabde ¹

Affiliations
1 Nagpur University, IN

Abstract

This paper may be regarded as a continuation of two of my previous papers. We obtain here a number of results involving the confluent hypergeometric functions such as the k_n-functions, D_n-functions, Laguerre polynomials and the Bessel functions. For some results the methods of the operational calculus have been used.

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N. G. Shabde ¹

Affiliations
1 College of Science, Nagpur, IN

Abstract

The object of this paper is to obtain a number of results involving Bateman's k_n-functions. We first note integrals of a general type, from which can be derived as particular cases several known results. Finally, we derive some k_n-function formulae as particular cases of results obtained by Erdelyi in two recent papers. We record these formulae, as they have not been known explicitly for the Bateman-functions.

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N. G. Shabde ¹

Affiliations
1 College of Science, Nagpur, IN

Abstract

The object of this note is to obtain certain series and integrals involving k_n-functions. These formulae do not seem to have been noted before.

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N. G. Shabde ¹

Affiliations
1 College of Science, Nagpur, IN

Abstract

The object of this paper is to collect a number of results involving the confluent hypergeometric functions such as the k-functions, D_u functions, Laguerre functions and the Bessel functions. The results have been obtained either by the methods of operational calculus or otherwise and are believed to be new.

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N. G. Shabde ¹

Affiliations
1 College of Science, Nagpur, IN

Abstract

Identities between the field-equations in the general field-theory of Schouten and van Dantzig have been obtained in a recent paper by the author by using a theorem of Emmy Noether. The object of the present paper is to verify these identities by direct substitution and to show the connexion between these identities and those found by E. T. Whittaker between the field-equations of Einstein's General Relativity. An attempt is also made to introduce A, the universal constant, proportional to the square of the curvature of the world into the field equations and the identities.

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N. G. Shabde ¹

Affiliations
1 College of Science, Nagpur, IN

Abstract

The object of this paper is to collect a number of results involving k_n-functions. These formulae do not seem to have been noted explicitly as yet. Some of them are obtained by the methods of operational calculus and others are derived from formulae involving W_k,m or M_k,m functions and Laguerre or Sonine polynomials given by Erdelyi, Howell, Bailey and Bateman.

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M. Zia-ud-Din , N. G. Shabde

Abstract

Prof. G. N. Watson has recently revaluated the integral

∫J_μ(at) J_v(bt)e^-ct dt

This integral has an important application in finding the generating function of Jacobi Polynomials. It may, therefore, be worth while to consider in this note.

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