Generating functions for the Jacobi polynomial
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- by M. E. Cohen PDF
- Proc. Amer. Math. Soc. 57 (1976), 271-275 Request permission
Abstract:
Two theorems are proved with the aid of operator and series iteration methods. Special cases appear to give new and known generating functions for the Jacobi polynomial.References
- Fred Brafman, Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc. 2 (1951), 942–949. MR 45875, DOI 10.1090/S0002-9939-1951-0045875-2
- J. W. Brown, New generating functions for classical polynomials, Proc. Amer. Math. Soc. 21 (1969), 263–268. MR 236438, DOI 10.1090/S0002-9939-1969-0236438-8 —, New generating functions for classical polynomials, Notices Amer. Math. Soc. 16 (1969), 412. Abstract #69T-B29.
- L. Carlitz, Some generating functions for Laguerre polynomials, Duke Math. J. 35 (1968), 825–827. MR 240351
- M. E. Cohen, On expansion problems: new classes of formulas for the classical functions, SIAM J. Math. Anal. 7 (1976), no. 5, 702–712. MR 442305, DOI 10.1137/0507053
- Ervin Feldheim, Relations entre les polynomes de Jacobi, Laguerre et Hermite, Acta Math. 75 (1943), 117–138 (French). MR 12724, DOI 10.1007/BF02404102
- H. M. Srivastava and J. P. Singhal, New generating functions for Jacobi and related polynomials, J. Math. Anal. Appl. 41 (1973), 748–752. MR 326028, DOI 10.1016/0022-247X(73)90244-8
- H. M. Srivastava, A class of generating functions for generalized hypergeometric polynomials, J. Math. Anal. Appl. 35 (1971), 230–235. MR 277776, DOI 10.1016/0022-247X(71)90247-2
- H. M. Srivastava, Generating functions for Jacobi and Laguerre polynomials, Proc. Amer. Math. Soc. 23 (1969), 590–595. MR 249694, DOI 10.1090/S0002-9939-1969-0249694-7 G. Szegö, Orthogonal polynomials, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 21 #5029.
- Arun Verma, On generating functions of classical polynomials, Proc. Amer. Math. Soc. 46 (1974), 73–76. MR 344537, DOI 10.1090/S0002-9939-1974-0344537-7
- David Zeitlin, A new class of generating functions for hypergeometric polynomials, Proc. Amer. Math. Soc. 25 (1970), 405–412. MR 264123, DOI 10.1090/S0002-9939-1970-0264123-3
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 271-275
- MSC: Primary 33A65
- DOI: https://doi.org/10.1090/S0002-9939-1976-0404725-X
- MathSciNet review: 0404725