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Summability of the Heine and Neumann Series of Legendre Polynomials

Published online by Cambridge University Press:  20 November 2018

Amnon Jakimovski
Amnon Jakimovski*
Affiliation:
Tel-Aviv University
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With a holomorphic function f(z) defined in a domain H which includes the closed interval [—1, 1] we associate the Neumann series

1

where Pn(z), Qn(t) are, respectively, the nth Legendre polynomials of the first and second kind and γ is a closed and rectifiable Jordan curve which includes [— 1, 1] in its interior and is included, together with its interior, in H.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1261 - 1263
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Jakimovski, A., Analytic continuation and summability of series Legendre polynomials, Quart. J. Math. Oxford, Ser. 2, 15 (1964), 289–302.Google Scholar
2. Powell, R. E., The L(r, t) summability transform, Can. J. Math., 18 (1966), 1251–1260.Google Scholar
3. Whittaker, R. E. and Watson, G. N., A course of modern analysis (Cambridge, 1946).Google Scholar