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Special Functions and Orthogonal Polynomials
| Content Provider | Scilit |
|---|---|
| Author | Coleman, Matthew P. |
| Copyright Year | 2016 |
| Description | T ′′ + c2λT = 0, Θ′′ + γΘ = 0, R′′ + 1 r R′ + ( λ− γ r2 ) R = 0, where T = T (t), Θ = Θ(θ) and R = R(r), and λ and γ are separation constants. The R-ODE is the eigenvalue version of Bessel's equation. c) Use Exercise 18 in Section 1.7 to conclude that γ = m2, where equation in the standard form of Bessel's equation of order α, x2y′′ + xy′ + (x2 − α2)y = 0 (where, for the vibrating membrane, of course, α = m = 0, 1, 2, . . .). e) If, instead, λ < 0, use the change of variable x = √−λ r to rewrite Book Name: An Introduction to Partial Differential Equations with MATLAB |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2011-0-15746-3&isbn=9780429112317&doi=10.1201/b15058-18&format=pdf |
| Ending Page | 340 |
| Page Count | 50 |
| Starting Page | 291 |
| DOI | 10.1201/b15058-18 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2016-04-19 |
| Access Restriction | Open |
| Subject Keyword | Book Name: An Introduction To Partial Differential Equations with Matlab Functions Orthogonal Polynomials C2λt |
| Content Type | Text |
| Resource Type | Chapter |
