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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 6 | Number 2 | Year 2014 | Article Id. IJMTT-V6P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V6P515

Appell Transforms Associated With Expansions in Terms of Generalized Heat Polynomials


B.B.Waphare
Abstract

In this paper we have discussed the regions of convergence of the series Σ∞n=0 anpn,α,β and Σ∞n=0 bn Wn,α,β (x1t).We have also discussed the class H*of generalized temperature functions having the Huygens property. Finally expansions for generalized temperature functions in terms of polynomials are derived and criteria for the expansions of functions in terms of Wn,α,β (x1t) is also established.

Keywords
Generalized heat polynomials, Appell transforms, generalized temperature function, Huygens property
References

[1] H. Bateman and A.Erdelyi, Higher transcendental functions, Vol. II, 1953.
[2] F.M. Cholewinski and D.T. Haimo, The Weierstrass-Hankel convolution transform, J. Analyse Math. (to appear).
[3] E.T. Copson, An introduction to the theory of a complex variable, 1935.
[4] D.T. Haimo, Integral equations associated with Hankel convolutions, Trans. Amer. Math. Soc., 116 (1965), 330-375.
[5] D.T. Haimo, Generalized temperature functions, Duke Math. J. (to appear).
[6] D.T. Haimo, Functions with the Huygens property, Bull. Amer. Math. Soc. 91 (1965), 528-532.
[7] I.I. Hirschman Jr. Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960-61), 307-336.
[8] P.C. Rosenbloom and D.V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc., 92 (1959), 220-266.
[9] D.V. Widder, Series expansions of solutions of the heat equation in dimensions, Annali di Matematica, 55 (1961), 389-409.
[10] J.N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge, 1958.

Citation :

B.B.Waphare, "Appell Transforms Associated With Expansions in Terms of Generalized Heat Polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 6, no. 2, pp. 149-175, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V6P515

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