Volume 33 | Number 4 | Year 2016 | Article Id. IJMTT-V33P533 | DOI : https://doi.org/10.14445/22315373/IJMTT-V33P533
Frédéric Ayant, "Some finite integrals and Fourier serie involving general class of polynomials, biorthogonal polynomials, Aleph-function and the multivariable Aleph-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 4, pp. 248-258, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P533
In this document, we obtain four integrals and four Fourier series expansions involving the multivariable Aleph-function, the general class of polynomials, biorthogonal polynomials and Aleph-function which are the sufficiently general in nature and are capable of yielding a large number of simpler and useful results merely by specializing the parameters in them. Further we establish some special cases.
[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 the Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220
[3] Prabhakar T.R. and Tomar R.C. Some integrals and series relations for biorthogonal polynomials suggested by Legendre polynomials. Indian. J. Pure. Appli. Math. Vol(11(7), 1980, page 863-869.
[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 multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. Vol 77(1985), page183-191
[7] 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.
[8] Tyagi A . A study of special functions and integral transforms with their applications. Ph.D. University of Rajasthan, Jaipur, India (1992).