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New connection formulae between ultraspherical polynomials and Chebyshev polynomials of third and fourth kinds

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초록

Four new analytical formulae expressing explicitly the connec- tion formulae between ultraspherical polynomials and Chebyshev polynomi- als of third and fourth kinds are given. Several relations among the four kinds of Chebyshev polynomials and Legendre polynomials are deduced as special cases. Some trigonometric identities, new closed forms for summing some terminating hypergeometric functions of unit argument and new closed formulae for four de nite integrals involving the product of ultraspherical and Chebyshev polynomials are also given.

Abstract

Four new analytical formulae expressing explicitly the connec- tion formulae between ultraspherical polynomials and Chebyshev polynomi- als of third and fourth kinds are given. Several relations among the four kinds of Chebyshev polynomials and Legendre polynomials are deduced as special cases. Some trigonometric identities, new closed forms for summing some terminating hypergeometric functions of unit argument and new closed formulae for four de nite integrals involving the product of ultraspherical and Chebyshev polynomials are also given.

참고문헌 (22)

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