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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
30.8. Airy Functions 1529
30.8 Airy Functions
30.8.1 Definitio n and Basic Formulas
Airy functions of the first and th e second kinds.
The Airy function of the first kind , Ai(x), and the Airy function of the second kind, Bi(x),
are solutions of the Airy equation
y
′′
xx
xy = 0
and are defined by the formulas
Ai(x) =
1
π
Z
0
cos
1
3
t
3
+ xt
dt,
Bi(x) =
1
π
Z
0
exp
1
3
t
3
+ xt
+ sin
1
3
t
3
+ xt

dt.
Wronskian: W {Ai(x), Bi(x)} = 1.
Relation to the Bessel functions and the modified Bessel functions.
Ai(x) =
1
3
x
I
1/3
(z) I
1/3
(z)
= π
1
q
1
3
x K
1/3
(z), z =
2
3
x
3/2
,
Ai(x) =
1
3
x
J
1/3
(z) + J
1/3
(z)
,
Bi(x) =
q
1
3
x
I
1/3
(z) + I
1/3
(z)
,
Bi(x) =
q
1
3
x
J
1/3
(z) J
1/3
(z)
.
30.8.2 Power
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Publisher Resources

ISBN: 9781466581494