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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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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
image (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

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