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The expansion of functions in ultraspherical polynomials

Published online by Cambridge University Press:  09 April 2009

David Elliott
David Elliott
Affiliation:
Mathematics Department, University of Adelaide, Adelaide, S.A.
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The ultraspherical polynomial (x) of degree n and order λ is defined by for n = 0, 1, 2, …. Of these polynomials, the most commonly used are the Chebyshev polynomials Tn(x) of the first kind, corresponding to λ = 0; the Legendre polynomials Pn(x) for which λ = ½; and the Chebyshev polynomials Un(x) of the second kind (λ = 1). In the first case the standardisation is different from that given in equation (1), since.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 4 , December 1960 , pp. 428 - 438
Copyright
Copyright © Australian Mathematical Society 1960

References

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