appendix B, Transcendental Functions

from: Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, Second

Author(s): Richard J. Sasiela

Published: 21 May 2007

Chapter DOI: http://dx.doi.org/10.1117/3.741372.apb

Chapter Page Count: 4 pages

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Front Matter

1. Introduction

2. Basic Equations for Wave Propagation in Turbulence

3. Filter Functions

4. Zero-Parameter Problems

5. Integral Evaluation with Mellin Transforms

6. Examples with a Single Positive Parameter

7. Strehl Ratio

8. Mellin Transforms with a Complex Parameter

9. Finite Beam Characteristics As Examples with a Single Complex Parameter

10. Mellin Transforms in N Complex Planes

11. Integral Evaluation with N Parameters

12. Beam Shape

A. Additional Mellin Transforms

B. Transcendental Functions

Back Matter

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Excerpt

This appendix contains the definitions of functions whose Mellin transforms are given in App. A. If an expression contains gamma functions, it is not valid for arguments that give an infinite result. For functions of the form ₂F₁ [a, b; c, z] the expression is only valid when |z| < 1.

http://dx.doi.org/10.1117/3.741372.apb

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