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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
Integration in Series 6-53
10. (a)
2
01 0
1
.
2
J J dx J=
(b)
01
() ().
a
xJ x dx J a
λλ
λ
=
11.
0
( ) cos( sin ) .
n
Jx x xd
π
πθθθ
=−
12.
321
2
() () ().Jxdx Jx Jx
x
=−
[JNTU 2003 (Set 2)]
6.3 CHEBYSHEV POLYNOMIALS
One of the important differential equations that gives rise to special
functions is the Chebyshev differential equation
22
(1 ) 0xy xy xy−−+=
′′
(6.115)
where n is a positive integer.
The singularities of Eq. (6.115) are 1.x
If we seek a power series solution of Eq. (6.115) about
0x =
of the form
0
()
m
m
m
yx cx
=
=
(6.116)
then this series solution is convergent in
1x <
since the distance
between
0x =
and the nearest singularity is 1. Differentiating ...
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Publisher Resources

ISBN: 9781299487406Publisher Website