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A simple method of establishing relations between Theta-functions of zero argument

Published online by Cambridge University Press:  20 January 2009

J. P. Dalton
J. P. Dalton
Affiliation:
University of the Witwatersrand, Johannesburg, South Africa.
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In connection with their proof of the fundamental relation

Whittaker and Watson state that “several proofs of this important proposition have been given, but none are simple.”

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 4 , August 1933 , pp. 286 - 288
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

page 286 note 1 For convenience, argument and parameter to be attached to each vacant Theta symbol are placed in front of each equation. Accents invariably indicate differentiation with respect to the argument v.

page 286 note 2 Whittaker, and Watson, : Modern Analysis (Cambridge, 1920), 470, footnote.Google Scholar

page 286 note 3 Whittaker, and Watson, : loc. cit., 477Google Scholar