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Generalized forms of the Series of Bessel and Legendre*

Published online by Cambridge University Press:  20 January 2009

Rev. F. H. Jackson
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Extract

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The object of this paper is to investigate certain series and differential equations, generalizations of the series of Bessel and Legendre.

Throughout the paper

reducing, when p = 1, to n.

The series discussed are the following:—

a generalized form of Pn(x),

the relation between coefficients of x in successive terms being

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , February 1902 , pp. 65 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1902

Footnotes

*

A short paper containing some of the results in this paper was read at the November meeting of the Society ; the paper, in its present form, is dated January 1903.

References

page 65 note * A short paper containing some of the results in this paper was read at the November meeting of the Society; the paper, in its present form, is dated January 1903.

page 66 note * Vol. XXVIII., Proceedings London Mathematical Society, p. 479.