Abstract
A fractional integral formula of Erdélyi is used to show that the fractional calculus leads in a natural way to useful formulas of the Dirichlet-Mehler type for the Jacobi polynomials and the generalized Legendre functions. Some important applications are pointed out, and a discrete analogue of Erdélyi's formula is derived and used to obtain a discrete Dirichlet-Mehler type formula for the Hahn polynomials (a discrete analogue of the Jacobi polynomials).
Supported in part by NSF Grant GP-32116. The author is an Alfred P. Sloan fellow.
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© 1975 Springer-Verlag
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Gasper, G. (1975). Formulas of the dirichlet-mehler type. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067105
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DOI: https://doi.org/10.1007/BFb0067105
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