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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
1534 SPECIAL FUNCTIONS AND THEIR PROPERTIES
30.9.3 Whittaker Functions
The Whittaker functions M
k,µ
(x) and W
k,µ
(x) are linearly independent solutions of the
Whittaker equation:
y
′′
xx
+
1
4
+
1
2
k +
1
4
µ
2
x
2
y = 0.
The Whittaker functions are expressed in terms of degenerate hypergeometric functions as
M
k,µ
(x) = x
µ+1/2
e
x/2
Φ
1
2
+ µ k, 1 + 2µ; x
,
W
k,µ
(x) = x
µ+1/2
e
x/2
Ψ
1
2
+ µ k, 1 + 2µ; x
.
30.10 Hypergeometric Functions
30.10.1 Various Representations o f the Hypergeometric Function
Representations of the hypergeometric function via hypergeometric series.
The hypergeometric function F (α, β, γ; x) is a solution of the Gaussian hypergeometric
equation ...
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Publisher Resources

ISBN: 9781466581494