One of the important differential equations that gives rise to special
functions is the Chebyshev differential equation
22
(1)0xyxyxy−−+=
′′′
(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
yxcx
∞
=
=
∑
(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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