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On Riesz logarithmic summability of the ultraspherical series

Published online by Cambridge University Press:  24 October 2008

G. S. Pandey
G. S. Pandey
Affiliation:
Vikram University, Ujjain, India
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Extract

Let f{θ, φ) be a function defined for the range 0 ≤ φ π, 0 ≤ φ ≤ 2π on a sphere S. The ultraspherical series associated with this function is

where

and the ultraspherical polynomials are defined by the following expansion

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 161 - 170
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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