unknown function f(n) satisfies: - -ns = f", f(0) = 1, f → 0 as n→ 0. With a = 0 this is the Rayleigh problem. Show that in this case the solution is f(n) = 1 – erf () where the error function is defined by 2 erf(x) = exp(-t²) dt. Also find a solution for the case a = : Hint: Try f(n) ~ n^ as a first soln, and then find a second solution using the first.
unknown function f(n) satisfies: - -ns = f", f(0) = 1, f → 0 as n→ 0. With a = 0 this is the Rayleigh problem. Show that in this case the solution is f(n) = 1 – erf () where the error function is defined by 2 erf(x) = exp(-t²) dt. Also find a solution for the case a = : Hint: Try f(n) ~ n^ as a first soln, and then find a second solution using the first.
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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