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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
Chapter 2 5
Elementar y Functions
and Their Properties
Throughout Chapter 25 it is assumed that
n
is a positive integer unless otherwise spec-
ified.
25.1 Power, Exponential, and Logarithmic Functions
25.1.1 Properties of the Power Function
Basic properties of the power function:
x
α
x
β
= x
α+β
, (x
1
x
2
)
α
= x
α
1
x
α
2
, (x
α
)
β
= x
αβ
,
for any α and β, where x > 0, x
1
> 0, x
2
> 0.
Differentiation and integration formulas:
(x
α
)
= αx
α1
,
Z
x
α
dx =
x
α+1
α + 1
+ C if α 6= 1,
ln |x| + C if α = 1.
The Taylor series expansion in a neighborhood of an arbitrary point:
x
α
=
X
n=0
C
n
α
x
αn
0
(x x
0
)
n
for |x x
0
| < |x
0
|,
where C
n
α
=
α(α 1) . . . (α n + 1)
n!
are binomial coefficients.
25.1.2 Properties ...
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Publisher Resources

ISBN: 9781466581494