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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 1 | Year 2016 | Article Id. IJMTT-V36P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P503

Integral involving the multivariable Aleph-function, a general class of polynomial, Aleph-function and integral function of two complex variables


F.Y . Ayant
Abstract

The object of this paper is to evaluate an integral involving the Laguerre polynomial and an integral function of two complex variables of order , based on the properties of the Aleph-function, general class of polynomials and multivariable Aleph-function. Further we establish some special cases.

Keywords
Aleph-function of several variables, general class of polynomials, Aleph-function of one variable, Aleph-function of two variables, Ifunction of several variables, I-function of two variables, integral function of two complex variables of order.
References

[1] Ayant F.Y. An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 2016 Vol 31 (3), page 142-154.
[2] 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.
[3] Copson E.T. Theory of functions of complex variable. Oxford, 1961
[4] Dzrbasjan M.M. On the integral representation and expansion in generalized Taylor series of entire functions of several complex variables. Mathematickeskii Sbornik 41 (83) , (157) , page 257 ( Russia).
[5] Gradshteyn L.S and Ryzhik I.M. Tables of integrals, series and products. Academic Press, New-York 1965
[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.
[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 :

F.Y . Ayant, "Integral involving the multivariable Aleph-function, a general class of polynomial, Aleph-function and integral function of two complex variables," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 1, pp. 17-26, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P503

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