Certain finite integrals pertaining to generalized polynomial set, a class of polynomials, Aleph-function and the multivariable Aleph-function

Frédéric Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V31P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 31 | Number 3 | Year 2016 | Article Id. IJMTT-V31P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V31P521

Certain finite integrals pertaining to generalized polynomial set, a class of polynomials, Aleph-function and the multivariable Aleph-function

Frédéric Ayant

Abstract

Our aim is to evaluate four integrals pertaining to the products of Aleph-function, a generalized polynomial set , a class of polynomial and the multivariable Aleph-function. On account of the most general nature of the function involved herein a very large number of known and new integrals involving simpler special functions and orthogonal polynomials follows as particular cases of our main integrals.

Keywords

Aleph-function of several variables, Aleph-function, finite integral, special function, general class of polynomials.

References

[1] Anil Goyal and R.D. Agrawal : Integral involving the product of I-function of two variables. Journal of M.A.C.T. 1995 ,vol.28 , page 147-155.
[2] Anil Goyal and R.D. Agrawal : Integration of I_function of two variables with respect to parameters. Jnanabha 1995 , vol.25 , page 87-91.
[3] Anil Goyal and R.D. Agrawal : on integration with respect to their parameters. Journal of M.A.C.T. 1995 , vol.29 page177-185.
[4] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[5] Raizada S.K. A study of unified representation of special functions of Mathematics Physics and their use in statistical and boundary value problem. Ph.D. Thesis, Bundelkhand University, Jhansi, India, 1991
[6] Sharma C.K. and Ahmad S.S. : On the multivariable I-function. Acta ciencia Indica Math , 1992 vol 20, 1994, page 113-116
[7] K. Sharma , On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences , Vol 3 , issue1 ( 2014 ) , page 1-13.
[8] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page183-191.
[9] Srivastava, H.M., Gupta, K.C. and Goyal, S.P.; The H-functions of One and Two Variables with Applications, South Asian Publishers, New Delhi and Madras (1982).
[10] Südland N.; Baumann, B. and Nonnenmacher T.F. , Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): 401-402.

Citation :

Frédéric Ayant, "Certain finite integrals pertaining to generalized polynomial set, a class of polynomials, Aleph-function and the multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 31, no. 3, pp. 129-141, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V31P521