[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c150228

CERTAIN INTEGRAL FORMULAS ASSOCIATED WITH ALEPH (ℵ)-FUNCTION

Agarwal, Praveen (Department of Mathematics Anand International College of Engineering)
Jain, Shilpi (Department of Mathematics Poornima College of Engineering)
Karimov, Erkinjon T. (Institute of Mathematics named after V. I. Romanovsky Academy of Sciences)
Prajapati, Jyotindra C. (Faculty of Technology and Engineering Marwadi Education Foundation Group of Institutions)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.2, 2017 , pp. 305-319 More about this Journal

Abstract

Recently many authors have investigated so-called Aleph ( ${\aleph}$ )-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph ( ${\aleph}$ )-function. Precisely, integrals with product of Aleph ( ${\aleph}$ )-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Keywords

Aleph function; I-function; H-function; Jacobi polynomials; Legendre function; Bessel Maitland function; hypergeometric function;

Citations & Related Records

Reference

1	J. Choi and D. Kumar, Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials, J. Inequal. Appl. 2014 (2014), 499, 15 pp. DOI
2	Y. Khan and P. Sharma, Some integral properties of Aleph function, general class of polynomials associated with Feynman integrals, IJMSI 2 (2014), no. 1, 21-27.
3	A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol. I, II, McGraw-Hill, New York-Toronto-London, 1953.
4	V. S. Kiryakova, Generalized fractional calculus and applications, Pitamat Research Notes in Mathematics, 301, Johan Wiley and Sones, New York, 1994.
5	A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Vol. 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York, 2006.
6	A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Halsted Press (John Wiley & Sons), New York, London, Sydney, Toronto, 1978.
7	A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function: Theory and Applications, Springer, New York, 2010.
8	E. D. Rainville, Special Function, The Macmillan Company, New York, 1960.
9	R. K. Saxena and T. K. Pogany, Mathieu-type series for the $\aleph$ -function occurring in Fokker-Planck equation, Eur. J. Pure Appl. Math. 3 (2010), no. 6, 980-988.
10	R. K. Saxena and T. K. Pogany, On fractional integral fromulae for $\aleph$ -function, Appl. Math. Comput. 218 (2011), 985-990.
11	N. Sudland, B. Baumann, and T. F. Nannenmacher, Open problem: Who knows about the $\aleph$ -function?, Appl. Anal. 1 (1998), no. 4, 401-402.
12	V. P. Saxena, Formal solution of certain new pair of dual integral equations involving H-function, Proc. Nat. Acad. Sci. India Sect. A51 (2001), 366-375.
13	H. M. Srivastava, A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Mat. 117 (1985), no. 1, 183-191. DOI
14	H. M. Srivastava and N. P. Singh, The integration of certain of product multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo Ser. 2 32 (1983), 157-187. DOI
15	N. Sudland, B. Baumann, and T. F. Nannenmacher, Fractional driftless Fokker-Planck equation with power law diffusion coefficients, in V. G. Gangha, E. W. Mayr, W. G. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing, 513-525 (CASC Konstanz 2001), Springer, Berlin, 2001.