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The Elliptic Integrals of the Third Kind

Published online by Cambridge University Press:  20 November 2018

E. H. Neville
E. H. Neville*
Affiliation:
Sonning-on- Thames, England
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This paper develops a case for adopting as the standard elliptic integrals of the third kind the function IIs(u, a) defined by

and the three functions lIs (u, a + Kc), Πs(u, a + Kn), Πss(u, a+ Kn) where KC, Kn, Kn are the three quarter-periods of the Jacobian system. The function Πs(u, a) is the same function whether qs u is cs u, ns u, or ds u.

The origin of the paper was a wish to understand how it has come about that the integrals commonly accepted as standard are not related symmetrically to the theta functions in terms of which they are expressed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 175 - 194
Copyright
Copyright © Canadian Mathematical Society 1959

References

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