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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
6-2 Diff erential Equations
Power series
An infi nite series of the form
0010
0
() ()
m
m
m
axx a ax x
=
−=+−+
2
20
()ax x−+
where
012
,,,aaa are real constants is called a power
series. These constants are called the coeffi cients of the series.
0
x
is a
constant and is called the centre of the series, and x is a real variable.
For the choice
0
0,x = we obtain the power series
2
01 2
0
m
m
m
ax a ax ax
=
=+ + +
(6.1)
with the origin as its centre.
Convergence interval
If there exists a positive real number R such that for all x in
(,)IxRxR=− +
the series Eq. (6.1) is convergent, then I is called
the interval of convergence for the series Eq. (6.1) and R is called ...
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Publisher Resources

ISBN: 9781299487406Publisher Website