Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions

Aleksandar Ivić: Definite Integration using the Generalized Hypergeometric Functions

Published $1977$, Massachusetts Institute of Technology.

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hosted by MIT

Contents

Chapter 1. INTRODUCTION

1.1. OVERVIEW OF OUR APPROACH

Chapter 2. SPECIAL AND GENERALIZED FUNCTIONS. STAGES I-II

2.1. THE FIRST STAGE

2.2. THE SECOND STAGE

Chapter 3. THE REDUCTION STAGE

3.1. GENERAL REDUCTION TESTS

3.2. SPECIAL REDUCTION TESTS

3.2.1. EXPONENTIAL BINOMIAL AND BESSEL REDUCTIONS

3.2.2. CONFLUENT HYPERGEOMETRIC FUNCTION REDUCTIONS

3.2.3. GAUSS HYPERGEOMETRIC FUNCTIONS REDUCTIONS

3.2.3.1. THE LIMIT-REDUCTION METHOD

3.2.3.2. LOGARITHMIC AND OTHER ALGEBRAIC CASES

3.2.3.3. LEGENDRE FUNCTION REDUCTIONS

3.2.3.4. THE ORTHOGONAL POLYNOMIALS OF JACOBI GEGENBAUER LEGENDRE AND TCHEBICHEF

3.2.3.5. INCOMPLETE BETA FUNCTION REDUCTIONS

3.2.4. OTHER REDUCTIONS

Chapter 4. CONCLUSIONS AND FURTHER RESEARCH

References

Appendix 1

Appendix 2

Appendix 3