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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 37 | Number 2 | Year 2016 | Article Id. IJMTT-V37P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P514

A study of unified results involving a product of generalized Legendre's function, a general class of polynomials, Aleph-function with the multivariable Aleph-function


F.Y.Ayant
Abstract

In this paper an integral involving general class of polynomials, Legendre's associated function, Aleph-function and Aleph-function of several variables has been evaluated and an expansion formula for product of the general class of polynomials, Legendre's associated function, Alephfunction and Aleph-function of several variables has been established with the application of this integral. The result established in this paper are of general nature and hence encompass several particular cases.

Keywords
Multivariable Aleph-function, Aleph-function, Legendre's associated function, general class of polynomials, expansion formula.
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] Meulendbeld, B. and Robin, L.; Nouveaux resultats aux functions de Legendre’s generalisees, Nederl. Akad. Wetensch. Proc. Ser. A 64(1961), page 333-347
[4] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[5] 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.
[6] Srivastava H.M., A contour integral involving Fox's H-function. Indian J.Math. 14(1972), page1-6.
[7] 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.
[8] 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), p.119-137.
[9] 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, "A study of unified results involving a product of generalized Legendre's function, a general class of polynomials, Aleph-function with the multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 2, pp. 92-101, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P514

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