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Fundamentals of Optical Fiber Sensors by Ken Chin, Haiwen Cai, Ronghui Qu, Zujie Fang

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APPENDICES

APPENDIX 1: MATHEMATICAL FORMULAS

A1.1 Bessel Equations and Bessel Functions

The Bessel equation has two linearly independent solutions: the first and second kinds Bessel functions,  and  :

(A1.1) Numbered Display Equation

(A1.2) Numbered Display Equation

where  is gamma function; for an integer argument,   .

(A1.3) Numbered Display Equation

 is also called Neumann function. Their linear combinations are Hankel functions:

(A1.4a) Numbered Display Equation

(A1.4b) Numbered Display Equation

The modified Bessel equation ...

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