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On the application of the operational calculus to the expansion of a function in a series of Legendre's functions of the second kind

Published online by Cambridge University Press:  20 January 2009

D. P. Banerjee
D. P. Banerjee
Affiliation:
Anandamohan College, Mymensingh, Bengal.
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In the present note we shall obtain the expansion in a series of Legendre functions of the second kind of an integral function φ (ω) represented by Laplace's integral

where f (x) is an analytic function of x, regular in the circle

where an are constants and qn (ω) = in+1Qn (iω).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 7 , Issue 1 , October 1942 , pp. 1 - 2
Copyright
Copyright © Edinburgh Mathematical Society 1942

References

1 Watson, , Theory of Hessel functions (Cambridge, 1922), § 16, 11 (3).Google Scholar

2 Nicholson, , “Electrification of parallel circular discs.” Phil. Trans. Royal Soc. (A), 224 (1924), 315.CrossRefGoogle Scholar