Additional solutions of a weighted heat equation. (English) Zbl 1235.34003
Consider the differential equation
\[
{d\over dx}\Biggl[(1- x^2){dv\over dx}\Biggr]= -\lambda^2 v.\tag{\(*\)}
\]
In case \(\lambda^2= n(n+1)\), \((*)\) represents the Legendre’s differential equation. Using this fact, the author describes a method to calculate infinitely many solutions to \((*)\).
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
References:
| [1] | Rainville, E. D., Special Functions (1960), The Macmillan Company: The Macmillan Company New York · Zbl 0050.07401 |
| [2] | G.A. Bear, Legendre functions as solutions to the inhomogeneous heat equation, A Thesis in Mathematics, 1995.; G.A. Bear, Legendre functions as solutions to the inhomogeneous heat equation, A Thesis in Mathematics, 1995. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
