Abstract
A Toeplitz transformation of a class of sequences is considered, in which the coefficients are multiples of shifted Jacobi polynomials, and depend upon a parameter. When the parameter is equal to +1, the transformation is not regular and is best applied to monotonic sequences [6]. When the parameter is equal to −1, the transformation is regular, and best applied to alternating sequences. In general, the transformation yields rational approximations. In the particular case of a logarithmic series, the rational approximations are precisely the [ n, n] Padé approximants; a particular case of a result of Luke [2]. Numerical examples are given, and errors estimated.
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