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Chapter 12: Q6P (page 591)

To show N(2n+1)(x)=(-1)n+1J-2n+1(x).

Short Answer

Expert verified

It is proved thatN(2n+1)(x)=(-1)n+1J-(2n+1)(x)

Step by step solution

01

Concept of Neumann Function:

The Neumann function:

Np(x)=cos(蟺辫)Jp(x)-J-p(x)sin(蟺辫)

02

Calculation of the function N(n+12)(x) :

Consider the Neumann function as follows:

Np(x)=cos(蟿蟿辫)Jp(x)-J-p蟿蟿辫sin蟿蟿辫Nn+12(x)=cos(n+12)蟿蟿辫Jn+12x-J-n+12sin蟿蟿辫n+12

=cos苍蟿蟿+蟿蟿2Jn+12(x)-J-n+12si苍蟿蟿n+12=-J-n+12x-1n

Simplify further as follows:

Nn+12(x)=-1n+12Jn+12(x)

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