Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

Appendix II

Mathematical formulas [1,2]

Abstract

This chapter presents the functions and formulas used in this text.

In the following formulas, m and n are integers, and μ and ν can have any value.

Binomial theorem

( 1 ± x ) n = ∑ m = 0 n ( ± 1 ) m ( n m ) x m = ∑ m = 0 n ( ± 1 ) m n ! m ! ( n − m ) ! x m , any x , n positive integer

(A2.1)

( 1 ± x ) v = ∑ m = 0 ∞ ( ± 1 ) m Γ ( v + 1 ) m ! Γ ( v − m + 1 ) x m , 0 ≤ | x | < 1 , v ≠ − 1 , − 2 , − 3 , …

(A2.2)

( 1 ± x ) − 1 = ∑ m = 0 ∞