[35 pts) Bessel functions are a model case for showing how to discover properties and relations of functions from series by which they are defined. Bessel functions satisfy an incredibly large number of relationships. The derivative of J, (r) with respect to r can be expressed by J,-1(ar) or J,41(x) by the formulas (a) a" J,(a)'= a" J,-1(x) (b) [J,(x)' = -x-"J,+1(x) %3D Derive equations (a) and (b) using the Bessel function of the first kind of order v defined as Σ (-1)mr2m 22m+vm!T(v+ m + 1) J,(x) = x" %3D m30
[35 pts) Bessel functions are a model case for showing how to discover properties and relations of functions from series by which they are defined. Bessel functions satisfy an incredibly large number of relationships. The derivative of J, (r) with respect to r can be expressed by J,-1(ar) or J,41(x) by the formulas (a) a" J,(a)'= a" J,-1(x) (b) [J,(x)' = -x-"J,+1(x) %3D Derive equations (a) and (b) using the Bessel function of the first kind of order v defined as Σ (-1)mr2m 22m+vm!T(v+ m + 1) J,(x) = x" %3D m30
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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Transcribed Image Text:(35 pts Bessel functions are a model case for showing how to discover properties
and relations of functions from series by which they are defined. Bessel functions
satisfy an incredibly large number of relationships. The derivative of J, (r) with
respect to a can be expressed by J,-1(ar) or J,41(x) by the formulas
(a) [a J,(a)'= a" J,-1(x)
(b) [r J,(x)) = -x-"J,41(x)
%3D
Derive equations (a) and (b) using the Bessel function of the first kind
of order v defined as
Σ
(-1)m2m
22m+vm!I(v + m + 1)
J,(x) = r"
%3D
m=0
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