## Exponential-Bessel partial differential equation and Fox’s $$H$$-function.(English)Zbl 0827.35049

Summary: We present and solve a two dimensional exponential-Bessel partial differential equation and obtain a particular solution of it involving Fox’s $$H$$-function.

### MSC:

 35K10 Second-order parabolic equations 33C60 Hypergeometric integrals and functions defined by them ($$E$$, $$G$$, $$H$$ and $$I$$ functions) 35C10 Series solutions to PDEs
Full Text:

### References:

 [1] Andrews, L.C.Special functions for engineers and applied mathematicians, Macmillan Publishing Co., New York (1985). [2] Bajpai, S.D.Fourier series of generalized hypergeometric functions, Proc. Camb. Phil. Soc.65 (1969), 703-707. · Zbl 0172.35202 [3] Carslaw, H.S.and Jaeger, J.C.Conduction of heat in solids (2nd End.) , Clarendon Press, Oxford, 1986. · Zbl 0584.73001 [4] Erdélyi, A.Higher transcendental functions, Vol. 2, Mc Graw-Hill, New York (1953). · Zbl 0052.29502 [5] Fox, C.The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc.98 (1961), 395-429. · Zbl 0096.30804 [6] Luke, Y.L.Integrals of Bessel functions, Mc Graw-Hill, New York (1962). · Zbl 0106.04301 [7] Taxak, R.L.Some results involving Fox’s H-function and Bessel functions, Math. Ed. (Siwan), IV-3 (1970), 93-97. · Zbl 1195.33173
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.