1. Use of the Generating Function of the Bessel Polyomial Recall from class notes that cos x Jo(x) +2(-1)". Jan(x) , n=1 sin z = 2(-1)" J2n+1(x) . n=1 Use the generating function for the Bessel function to prove the two identities. You should give all the details. Hint: Set t = exp(ie) in the generating function and recall the trigonometric identity for exp(i0). %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Use of the Generating Function of the Bessel Polyomial
Recall from class notes that
cos x
Jo(x) +2(-1)". Jan(x) ,
n=1
sin z = 2(-1)" J2n+1(x) .
n=1
Use the generating function for the Bessel function to prove the two identities. You should
give all the details.
Hint: Set t = exp(ie) in the generating function and recall the trigonometric identity for
exp(i0).
%3D
Transcribed Image Text:1. Use of the Generating Function of the Bessel Polyomial Recall from class notes that cos x Jo(x) +2(-1)". Jan(x) , n=1 sin z = 2(-1)" J2n+1(x) . n=1 Use the generating function for the Bessel function to prove the two identities. You should give all the details. Hint: Set t = exp(ie) in the generating function and recall the trigonometric identity for exp(i0). %3D
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