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LAPLACE TRANSFORM OF SOME WELL KNOWN SPECIAL FUNCTIONS

Jyotindra C. Prajapati1, Bhailal P. Patel2
  1. Head, Department of Mathematical Sciences Charotar University of Science and Technology Changa, Anand-388421, Gujarat, India, E-mail: [email protected]
  2. Head, Department of Mathematical Sciences N.V. Patel College of Pure and Applied Sciences Vallabh Vidyanagar, Gujarat, India, E-mail: [email protected]
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Abstract

Integral Transforms draw the attention of many researchers and hence various types of Integral Transforms introduced time-to-time (Debnath [2], Snedon [4]). Integral Transforms play a key role in the field of Special Functions. In this paper, authors studied Laplace Transforms (this is one of the renowned Integral Transform) of several well-known Special Functions.

Keywords

Bessel's function, Hermite Polynomial, Hypergeometric function, Legendre Polynomials, Laguerre Polynomial, Laplace Transforms.

INTRODUCTION

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References

[ 1 ] Khan M.A.:A note on a polynomial set generated by G(2xt-t2) for the choice G(u) =0F1(-;α; u), Acta Ciencia Indica 28; 117-126; 2002.

[ 2 ] Lokenath Debnath: Intrgral Transforms and their applications, second edition, Chapman and Hall/CRC Taylor and Francis Group, 2007.

[ 3 ] Rainville E.D. Special Functions, Macmillan, New York, 1960.

[ 4 ] Sneddon,I.N., The Use of Integral transforms, McGraw-Hill Book Company, New York, 1972.

[ 5 ] Srivastava H.M. and manocha H.L.: A treatise on generating functions, John Wiley and Sons, New York, Ellis Horwood, Chichester, 1984.