Gegenbauer ODEs - Maple Help

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Gegenbauer ODEs

Description

• 

The general form of the Gegenbauer ODE is given by the following:

Gegenbauer_ode := (x^2-1)*diff(y(x),x,x)-(2*m+3)*x*diff(y(x),x)+lambda*y(x)=0;

Gegenbauer_ode:=x21ⅆ2ⅆx2yx2m+3xⅆⅆxyx+λyx=0

(1)
  

where m is an integer. See Infeld and Hull, "The Factorization Method". The solution of this type of ODE can be expressed in terms of the LegendreQ and LegendreP functions:

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorGegenbauer_ode

_Gegenbauer

(3)

dsolveGegenbauer_ode

yx=_C1x2154+12mLegendrePm2λ+4m+412,52+m,x+_C2x2154+12mLegendreQm2λ+4m+412,52+m,x

(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.


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