Solved Problems in Analysis

Name: Solved Problems in Analysis | As Applied to Gamma, Beta, Legendre and Bessel Functions
Brand: Dover Publications
Price: 33.99 EUR
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As Applied to Gamma, Beta, Legendre and Bessel Functions

Orin J. Farrell Bertram Ross(Autor*in)

Dover Publications (Verlag)

Erschienen am 6. November 2013

611 Seiten

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Inhalt

Cover
Title Page
Copyright Page
Contents
Introduction, Table and Graph
Integral Expressions of G(x) Probs. 1-3
Properties of G(x) Probs. 4, 10, 12-21, 31
Specific Evaluations of G(x) Probs. 5-9, 11, 22, 23
Infinite Product Expression of G(x) Prob. 24
Integral Expressions of B(x, y) Probs. 25, 27, 28
Properties of B(x, y) Probs. 26, 29, 30
G´(1) = Negative of Euler's Constant Prob. 32
Logarithmic Derivative of G(x) for Positive Integers Prob. 33
Chapter I The Gamma Function and the Beta Function
Chapter II Applications of the Gamma Function and the Beta Function
Introduction
Evaluation of Integrals Probs. 1-11, 14-27, 33, 35
Probs. 12, 13
Infinite Product Expression of p/2 Probs. 28, 29
Evaluation of Certain Geometrical Magnitudes Probs. 30-32, 34, 36-39
Evaluation of Certain Physical Quantities Probs. 36, 40-42
Approximation of n! for Large Integers Probs. 43-47
Two Problems in Probability Probs. 48-49
A Problem in Heat Flow in a Straight Wire Prob. 50
Chapter III Legendre Polynomials
Introduction
Coefficients in Expansion of a Generating Function Prob. 1
Recurrence Relations Probs. 2, 13-15, 23, 24
Laplace's Integral Expression of Pn(x) Prob. 3
Determination of Specific Legendre Polynomials Prob. 4-9
Rodrigues's Expression for Pn(x) Prob. 10
Orthogonality Property and Related Property Probs. 16, 17
Expansion of a Given Function in Legendre Polynomials |Pn(x)| ? 1 for -1 ? x ? 1 Probs. 11, 18, 19
Character and Location of Zeros of Pn(x) Prob. 12
Evaluation of Derivatives Prob. 25
Evaluation of Integrals Involving Legendre Polynomials Prob. 21
Chapter IV Applications of Legendre Polynomials
Introduction
Specific Series Expansions Probs. 1-8, 16, 17
Steady-state Heat-flow Temperature Distribution Probs. 9-13
Gravitational Potential of a Circular Lamina Prob. 14
Potential of an Electric Charge Distribution Prob. 15
Infinite Product Expression for p/2 Prob. 18
Application of Gauss's Mechanical Quadrature Formula with Pertinent Table Probs. 19-20
Chapter V Bessel Functions
Introduction
Differentiation Formulas Probs. 1-6, 8-10, 12, 15, 19
Recursion Formulas Probs. 7, 16
Specific Evaluations Probs. 13, 14
Functions of Orders Probs. 17, 18, 20
Alternation of Zeros Prob. 21
Generating Functions Probs. 22, 23
Orthogonality Property and Related Property Probs. 24, 25
Expansion of a Given Function in Bessel Functions Probs. 26, 27
Evaluation of Integrals Involving Bessel Functions Probs. 11, 28-33
Approximations for Small and Large Arguments Probs. 34, 35
Integral Expression of Jp(x) and of Jn(x) Probs. 36, 37
Relations to Legendre Polynomials Probs. 38-41
Introduction
Solutions of Equations Reducible to Bessel's Equation Probs. 1-6
Specific Expansions in Bessel Functions Probs. 7-10 Problems in Dynamics Probs. 11-17, 21, 22
Flux Distribution in a Nuclear Reactor Prob. 18
Heat-flow Temperature Distribution Probs. 19, 20, 24, 25, 30
Fluid Velocity Imparted by Radially Pulsating Cylinder Prob. 23
Displacement of Vibrating Annular Membrane Prob. 26
Alternating Current Density Prob. 27
Eddy Current Density and Power Loss Probs. 28, 29
Chapter VI Applications of Bessel Functions
Index

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