Volume 61 | Number 1 | Year 2018 | Article Id. IJMTT-V61P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P507
Gupta [5] and Gupta et al. [6] have studied the application of generalized prolate spheroidal wave function, generalized polynomials, and the multivariable H-function in heat conduction. In this paper we employ the generalized prolate spheroidal wave function, generalized hypergeometric function, class of multivariable polynomials and the multivariable Gimel-function in heat conduction in obtaining the formal solution of partial differential equation related to a problem of heat conduction in an anisotropic material. This problem occurs mainly in mechanics of solids, physics and applied mathematics.
[1] F. Ayant, An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT), 31(3) (2016), 142-154.
[2] F.Y .Ayant, Some transformations and idendities form multivariable Gimel-function, International Journal of Matematics and Technology (IJMTT), 59(4) (2018), 248-255.
[3] B.L.J. Braaksma, Asymptotics expansions and analytic continuations for a class of Barnes-integrals, Compositio Math. 15 (1962-1964), 239-341.
[4] Gupta R.K. Generalized prolate spheroidal wave functions. Proc. India. Acad. Sci 85A (2), (1977), page 104-114.
[5] Gupta V.G. The generalized prolate spheroidal wave function and its applications. Jnanabha. Vol 16, 1986, page 103-112.
[6] Gupta V.G. The application of generalized prolate spheroidal wave function, generalized polynomials and the multivariable H-function in heat conduction equation. Acta. Ciencia. Indica. Math. Vol 28, no 4, 2002, page 553-558.
[7] Gupta V.G., Kumari P. and Jain S. The application of generalized prolate spheroidal wave function, generalized polynomials and the multivariable H-function in linear flow in an anisotropic material. J. Rajasthan. Acad. Phy. Sci. Vol2, no 2, 2003, page 111-120.
[8] Y.N. Prasad, Multivariable I-function , Vijnana Parisha Anusandhan Patrika 29 (1986), 231-237. [9] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International
Journal of Engineering Mathematics Vol (2014), 1-12.
[10] V.P. Saxena and Nageria. Linear flow of heat in an anisotropic finite solid moving in a conducting medium. Jnanabha. Sect A 4, 1974, page 1-6.
[11] H.M. Srivastava, A multilinear generating function for Konhauser set of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117(1985), 183-191.
[12] H.M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24 (1975),119-137.
[13] H.M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25 (1976), 167-197.
[14] H.M. Srivastava and N.P. Singh, The integration of certains products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo. 32(2)(1983), 157-187.
F.Y.Ayant, "The Application of Generalized Prolate Spheroidal Wave Function, Class of Multivariable Polynomials, and the Multivariable Gimel-Function in Heat Conduction," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 1, pp. 51-57, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P507