×

Uh-oh, it looks like your Internet Explorer is out of date.

For a better shopping experience, please upgrade now.

On a Class of Incomplete Gamma Functions with Applications
     

On a Class of Incomplete Gamma Functions with Applications

by Syed M. Zubair, M. Aslam Chaudhry
 

ISBN-10: 1584881437

ISBN-13: 9781584881438

Pub. Date: 08/21/2001

Publisher: Taylor & Francis

The closed-form solutions to a considerable number of problems in appl ied mathematics, astrophysics, nuclear physics, and engineering can be expressed in terms of the incomplete Gamma functions. Focusing on sev eral heat conduction problems, this monograph provides a comprehensive study of incomplete Gamma functions. It describes the properties of t he class of

Overview

The closed-form solutions to a considerable number of problems in appl ied mathematics, astrophysics, nuclear physics, and engineering can be expressed in terms of the incomplete Gamma functions. Focusing on sev eral heat conduction problems, this monograph provides a comprehensive study of incomplete Gamma functions. It describes the properties of t he class of generalized Gamma functions, explores useful generalizatio ns and decompositions of the functions, and provides tabular and graph ical representations for numerical and scientific computations apart f rom their applications to heat conduction problems with time-dependent boundary conditions.

Product Details

ISBN-13:
9781584881438
Publisher:
Taylor & Francis
Publication date:
08/21/2001
Pages:
512
Product dimensions:
6.20(w) x 9.30(h) x 1.30(d)

Table of Contents

GENERALIZED GAMMA FUNCTION
The Gamma Fun ction G(a)
Definition of the Generalized Gamma Function
Properties of the Generalized Gamma Function
Mellin and Laplace Transforms
Asymptotic Representations
The Macdonald Function
The Digamma Function y(x)
Generalization of Psi (Digamma) Function
Integral Representations of yb (a)
Properties of the Generalized Psi Function
Graphical and Tabular Representations
THE GENERALIZED INCOMPLETE GAMMA FUNCTIONS
The Incomplete Gamma Functions
Definition of the Generalized Incomplete Gamma Functions
Properties of the Incomplete Generalized Gamma Functions
Convolution Representations and Laplace Transforms
Connection with Other Special Functions
KdF Functions and Incomplete Integrals
Representation in terms of KdF Functions
Reduction Formulas for F0:2;1 2:0;0[x,y]
Integrals of Product of Bessel and Gamma Functions
Asymptotic Representations
Integral Representation for G(a,x;b)
Graphical and Tabular Representations
THE FAMILY OF THE GAMMA FUNCTIONS
The Family of Incomplete Gamma Functions
The Generalized Error Functions
The Generalized Exponential Integral function
The Generalized Fresnel Integrals
The Decomposition Functions
The Extended Decomposition functions
The E(u,v) and F(u,v) Functions
The e(u) and f(u) Functions
Graphical and Tabular Representations
EXTENSION OF GENERALIZED INCOMPLETE GAMMA FUNCTIONS
Introduction
The Decomposition Formula
Recurrence Relations
Laplace and K-Transform Representation
Parametric Differentiation and Integration
Connection with Other Special Functions
Integral Representations
Differential Representations
The Mellin Transform Representation
EXTENDED BETA FUNCTION
The Beta Function
The Incomplete Beta Function
The Beta Probability Distribution
Definition of the Extended Beta Function
Properties of the Extended Beta Function
Integral Representations of the Extended Beta Function
Conncection with Other Special Functions
Representations in Terms of Whittaker functions
Extended Incomplete Beta Function
The Extended Beta Distribution
Graphical and Tabular Representations
EXTENDED INCOMPLETE GAMMA FUNCTIONS
Introduction
Definition of the Extended Incomplete Gamma Functions
The Decomposition Formula
Recurrence Formula
Connection with Other Special Functions
The H-Function
Incomplete Fox H-Functions
EXTENDED RIEMANN ZETA FUNCTIONS
Introduction
Bernoulli's Numbers and Polynomials
The Zeta Function
Zeros of the Zeta Function and the Function p(x)
The Extended Zeta Function z(a)
The Second Extended Zeta Function zb*(a)
The Hurwitz Zeta Function
Extended Hurwitz Zeta Functions
Extended Hurwitz Formulae
Further Remarks and Comments
Graphical and Tabular Representations
PHASE-CHANGE HEAT-TRANSFER
Introduction
Constant Temperature Boundary Conditions
Convective Boundary Conditions
Freezing of Tissues around a Capillary Tube
Freezing of Binary Alloys
Freezing Around an Impurity
Numerical Methods for Phase-Change Problems
HEAT CONDUCTION WITH TIME-DEPENDENT BOUNDARY CONDITIONS
Introduction
Time-Dependent Surface Temperatures
Time-Dependent Surface Heat Fluxes
Illustrative Example
HEAT CONDUCTION DUE TO TIME-DEPENDENT LASER SOURCES
Introduction
Mathematical Formulation
Some Cases of Practical Interest
A UNIFIED APPROACH TO HEAT SOURCE PROBLEMS
Introduction
Thermal Explosions
Continuously Operating Heat Sources
APPENDICES
Heat Conduction
Table of Laplace Transforms
Integrals Dependent of Parameters
REFERENCES
SYMBOLS
INDEX

Customer Reviews

Average Review:

Post to your social network

     

Most Helpful Customer Reviews

See all customer reviews