Appell Transforms Associated With Expansions in Terms of Generalized Heat Polynomials

  IJMTT-book-cover
 
International Journal of Mathematical Trends and Technology (IJMTT)          
 
© 2014 by IJMTT Journal
Volume-6 Number-2                          
Year of Publication : 2014
Authors : B.B.Waphare
  10.14445/22315373/IJMTT-V6P515

MLA

B.B.Waphare. "Appell Transforms Associated With Expansions in Terms of Generalized Heat Polynomials", International Journal of Mathematical Trends and Technology (IJMTT). V6:149-175 February 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper we have discussed the regions of convergence of the series Σn=0 anpn,α,β and Σn=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

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.

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