The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Generating Function of some Biorthogonal Polynomials Involving Stirling Numbers of Second Kind


Affiliations
1 Mudhoji College, Phaltan (M.S.), India
2 Y.C. Institute of Science, Satara (M.S.), India
     

   Subscribe/Renew Journal


In 1982 Madhekar and Thakare defined and studied a pair of biorthogonal polynomials {Jn(α, β, k; x)} and {Kn(α, β, k; x)} with respect to Jacobi weight function (1-x)α (1+x)β over the interval (-1, 1) where α > -1; β > -1 and k is positive integer. In the present paper some generating functions of biorthogonal polynomials of second set {Kn(α, β, k; x)} involving Stirling numbers of second kind are obtained by using Srivastava's method and some particular cases are also noted.

Keywords

Jacobi Weight Function, Biorthogonal Polynomials, Generating Function, Stirling Number.
Subscription Login to verify subscription
User
Notifications
Font Size


  • B. Gabutti and J. N. Lyness, Some generalizations of the Euler- knopp transformation, Number Math., 48(1986), 199-220.

  • J. D. E. Konhauser, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacic J. Math., 21(1967), 303-314.

  • H. C. Madhekar and N. K. Thakare, Biorthogonal polynomials suggested by the Jacobi polynomials, Pacic J. Math., 100(1982), 417-424.

  • H. C. Madhekar and N. K. Thakare, On obtaining multilateral generating functions, Indian J. Pure Appl. Math., 15(2)(1984-a), 149-160.

  • H. C. Madhekar and N. K. Thakare, Multilateral generating functions for biorthogonal polynomials suggested by Jacobi polynomials, Indian J. Pure Appl. Math., 15(2)(1984-b), 161-170.

  • M. L. Mathis and S. Sismondi, Alcune funzioni generatrici di-funzioni speciali, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 118(1984), 185-192.

  • H. M. Srivastava, Some families of generating functions associated with the Stirling numbers of the second kind, J. Math. Anal. Appl., 251(2000), 752-769.

  • H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, John wiley and Sons, New Yark, 1984.

  • N. K. Thakare and H. C. Madhekar, On the second set Kn(α, β, K, x) of biorthogonal polynomials suggested by Jacobi polynomials, Bull. Institute Math. Academia Sinica 12(4)(1984).


Abstract Views: 273

PDF Views: 0




  • Generating Function of some Biorthogonal Polynomials Involving Stirling Numbers of Second Kind

Abstract Views: 273  |  PDF Views: 0

Authors

N. M. Kavathekar
Mudhoji College, Phaltan (M.S.), India
T. B. Jagtap
Y.C. Institute of Science, Satara (M.S.), India

Abstract


In 1982 Madhekar and Thakare defined and studied a pair of biorthogonal polynomials {Jn(α, β, k; x)} and {Kn(α, β, k; x)} with respect to Jacobi weight function (1-x)α (1+x)β over the interval (-1, 1) where α > -1; β > -1 and k is positive integer. In the present paper some generating functions of biorthogonal polynomials of second set {Kn(α, β, k; x)} involving Stirling numbers of second kind are obtained by using Srivastava's method and some particular cases are also noted.

Keywords


Jacobi Weight Function, Biorthogonal Polynomials, Generating Function, Stirling Number.

References