Evaluate -ax fote Jo(bx) dx, a, b > 0. Actually the results hold for a ≥ 0, -∞ < b <∞o. This is a Laplace transform of Jo.
Evaluate -ax fote Jo(bx) dx, a, b > 0. Actually the results hold for a ≥ 0, -∞ < b <∞o. This is a Laplace transform of Jo.
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:12.1.13 Evaluate
Lo
e-ax Jo(bx) dx, a, b > 0.
Actually the results hold for a ≥ 0, -∞ < b <∞o. This is a Laplace
transform of Jo.
12.2 Neumann Functions, Bessel Functions of the Second Kind
611
Hint. Either an integral representation of Jo or a series expansion or
a Laplace transformation of Bessel's ODE will be helpful.
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