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For each positive integer n, the Bessel function J,(x) may be defined by (1-12)n-1/2 cos xt dt. J₁(x) 1.3.5 Prove that J,(x) satisfies Bessel's x" Jn" · (2n-1)π. +1 differential equation 1 n' + — ² + (1 - ²)√₁ -0. - X X

For each positive integer n, the Bessel function J,(x) may be defined by (1-12)n-1/2 cos xt dt. J₁(x) 1.3.5 Prove that J,(x) satisfies Bessel's x" Jn" · (2n-1)π. +1 differential equation 1 n' + — ² + (1 - ²)√₁ -0. - X X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.7 For each positive integer n, the Bessel function J,(x) may be defined by xn (1-12)n-1/2 cos xt dt. +1 J₁(x) = 1.3.5... Prove that J,(x) satisfies Bessel's differential equation (2n-1)πT √ Jn" Jn' - 1 1 + —- √² + (1 - ²)√₁ = 0. Jn X
Transcribed Image Text:3.7 For each positive integer n, the Bessel function J,(x) may be defined by xn (1-12)n-1/2 cos xt dt. +1 J₁(x) = 1.3.5... Prove that J,(x) satisfies Bessel's differential equation (2n-1)πT √ Jn" Jn' - 1 1 + —- √² + (1 - ²)√₁ = 0. Jn X
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