On the Summability of a Certain Class of Series of Jacobi Polynomials

Authors

A. P. Cowgill, University of Nebraska - Lincoln

Date of this Version

1935

Comments

Published in Bull. Amer. Math. Soc. 41 (1935) 541-549.

Abstract

The result obtained in this paper is as follows:
The series Σnⁱ[((p + 1)(p +3)…(p +2n -1)) ÷(2ⁿn!) X^((p-1)/2)_n (x), where X_n^(p-1)/2(x) (hereafter indicated simply by X_n) is a symmetric Jacobi polynomial p >-1, and i a positive integer, is summable (C, k),k>i—1/2, for the range -1 <x<1.