Finite integral involving the sequences of functions, a class of polynomials, multivariable Aleph-functions anf logarithm function of general arguments I

	International Journal of Mathematics Trends and Technology (IJMTT)
	© 2016 by IJMTT Journal
	Volume-36 Number-3
	Year of Publication : 2016
	Authors : F.Y.Ayant
	10.14445/22315373/IJMTT-V36P523

F.Y.Ayant "Finite integral involving the sequences of functions, a class of polynomials, multivariable Aleph-functions anf logarithm function of general arguments I", International Journal of Mathematics Trends and Technology (IJMTT). V36(3)145-156 August 2016. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In the present paper we evaluate a generalized finite integral involving the product of the sequence functions, the multivariable Aleph-functions general class of polynomials of several variables and logarithm function with general arguments. The importance of the result established in this paper lies in the fact they involve the Aleph-function of several variables which is sufficiently general in nature and capable to yielding a large of results merely by specializating the parameters their in.

References
[1] Agrawal B.D. And Chaubey J.P. Certain derivation of generating relations for generalized polynomials. Indian J. Pure and Appl. Math 10 (1980), page 1155-1157, ibid 11 (1981), page 357-359
[2] Brychkow Y.A. Handbook of Special Functions. Derivatives. Integrals, Series and Other Formulas. CRC. Press. Taykor and Francis Group. Boca. Raton. London. New York. 2008.
[3] Fujiwara I. A unified presentation of classical orthogonal polynomials. Math. Japon. 11 (1966), page133-148.
[4] 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
[5] Salim T.O. A serie formula of generalized class of polynomials associated with Laplace transform and fractional integral operators. J. Rajasthan. Acad. Phy. Sci. 1(3) (2002), page 167-176.
[6] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[7] C.K. Sharma and P.L. mishra : On the I-function of two variables and its properties. Acta Ciencia Indica Math , 1991, Vol 17 page 667-672.
[8] Sharma K. On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences , Vol 3 , issue1 ( 2014 ) , page1-13.
[9] 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. Personal adress : 411 Avenue Joseph Raynaud Le parc

Keywords
Multivariable Aleph-function, general class of polynomials, sequence of functions, multivariable I-function, Aleph-function of two variable, I-function of two variables.