|
Laguerre ODEs
|
|
Description
|
|
|
•
|
The general form of the Laguerre ODE is given by the following:
|
|
>
|
Laguerre_ode := x*diff(y(x),x,x)+(a+1-x)*diff(y(x),x)+lambda*y(x) = 0;
|
|
| (1) |
|
|
See Iyanaga and Kawada, "Encyclopedic Dictionary of Mathematics", p. 1481. The solution to this type of ODE can be expressed in terms of the WhittakerW and WhittakerM functions.
|
|
|
|
Examples
|
|
|
>
|
|
|
![[odeadvisor]](/support/helpjp/helpview.aspx?si=7241/file04357/math34.png)
| (2) |
|
>
|
|
|
![[_Laguerre]](/support/helpjp/helpview.aspx?si=7241/file04357/math41.png)
| (3) |
|
>
|
|
|
| (4) |
|
|
|
See Also
|
|
DEtools, odeadvisor, dsolve, and ?odeadvisor,<TYPE> where <TYPE> is one of: quadrature, missing, reducible, linear_ODEs, exact_linear, exact_nonlinear, sym_Fx, linear_sym, Bessel, Painleve, Halm, Gegenbauer, Duffing, ellipsoidal, elliptic, erf, Emden, Jacobi, Hermite, Lagerstrom, Laguerre, Liouville, Lienard, Van_der_Pol, Titchmarsh; for other differential orders see odeadvisor,types.
|
|
