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- W2017665552 abstract "A classical theorem on expansion of an analytic function in a series of Jacobi polynomials $P_n^{(alpha ,beta )} $ is extended so that $alpha $ and $beta $, instead of being assumed real, may have any complex values provided $alpha + beta ne - 2, - 3, - 4, cdots $. The function to be expanded may be analytic inside an arbitrary ellipse in the complex plane, since we use notation which does not fix the foci at $ -1 $ and 1. If the ellipse is a circle, Jacobi’s series reduces to Taylor’s series as a special case, not a limiting case. Cauchy’s inequality for the coefficients of Taylor’s series has an analogue for Jacobi's series. The coefficients are determined uniquely by the analytic function. Some special series are listed." @default.
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- W2017665552 date "1974-10-01" @default.
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- W2017665552 title "Expansion of Analytic Functions in Jacobi Series" @default.
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- W2017665552 doi "https://doi.org/10.1137/0505076" @default.
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