- 592 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Asymptotics and Special Functions
About this book
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
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Yes, you can access Asymptotics and Special Functions by Frank Olver in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.
Information
INTRODUCTION
TO
ASYMPTOTIC
ANALYSIS
1
Origin
of
Asymptotic
Expansions
1.1
Consider
the
integral
F(x)
=
re-'
cost
dr
for
positive
real
values
of
the
parameter
x.
Let
us
attempt
its
evaluation
by
expanding
cost
in
powers
of
t
and
integrating
the
resulting
series
term
by
term.
We
obtain
Provided
that
x
>
1
the
last
series
converges
to
the
sum
That
the
attempt
proved
to
be
successful
can
be
confirmed
by
deriving
the
last
result
directly
from
(1.01)
by
means
of
two
integrations
by
parts;
the
restriction
x
>
1
is
then
seen
to
be
replaceable
by
x
>
0.
Now
let
us
follow
the
same
procedure
with
the
integral
We
obtain
Table of contents
- Cover
- Title Page
- Copyright Page
- Dedication
- Table of Contents
- Preface to A K Peters Edition
- Preface
- 1: Introduction to Asymptotic Analysis
- 2: Introduction to Special Functions
- 3: Integrals of a Real Variable
- 4: Contour Integrals
- 5: Differential Equations with Regular Singularities; Hypergeometric and Legendre Functions
- 6: The Liouville–Green Approximation
- 7: Differential Equations with Irregular Singularities; Bessel and Confluent Hypergeometric Functions
- 8: Sums and Sequences
- 9: Integrals: Further Methods
- 10: Differential Equations with a Parameter: Expansions in Elementary Functions
- 11: Differential Equations with a Parameter: Turning Points
- 12: Differential Equations with a Parameter: Simple Poles and Other Transition Points
- 13: Connection Formulas for Solutions of Differential Equations
- 14: Estimation of Remainder Term
- Answers to Exercise
- Reference
- Index of Symbols
- General Inde