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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1554 SPECIAL FUNCTIONS AND THEIR PROPERTIES
Here, m, n = 0, ±1, ±2, . . .
Remark 30.1. The theta functions are not elliptic functions. The very good convergence of their
series allows the computation of various elliptic integrals and elliptic functions using the relations
given above in Section 30.15.1.
30.15.2 Various Relations and Formulas. Connection with Jacobi
Elliptic Functions
Linear and quadratic relations.
Linear relations (first set):
ϑ
1
v +
1
2
= ϑ
2
(v), ϑ
2
v +
1
2
= ϑ
1
(v),
ϑ
3
v +
1
2
= ϑ
4
(v), ϑ
4
v +
1
2
= ϑ
3
(v),
ϑ
1
v +
τ
2
= ie
v+
τ
4
ϑ
4
(v), ϑ
2
v +
τ
2
= e
v+
τ
4
ϑ
3
(v),
ϑ
3
v +
τ
2
= e
v+
τ
4
ϑ
2
(v), ϑ
4
v +
τ
2
= ie
v+
τ
4
ϑ
1
(v).
Linear relations (second ...
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Publisher Resources

ISBN: 9781466581494