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Spheroidal wave functions in MATHEMATICA & system of DE

Leslaw Bieniasz
Posted 11 years ago
POSTED BY: Leslaw Bieniasz
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Leslaw Bieniasz
Leslaw Bieniasz
Posted 11 years ago

Yes, but: 1) It is sufficient to omit the term with m^2 and this command will not work. I would argue this is strange and unexpected. 2) The command returns the general solution in terms of SpheroidalPS and SperoidalQS functions only, which is probably correct in the case of the first of my equations, but I need a general solution of the second equation as well. The latter is probably dependent on the functions SpheroidalS1 and SpheroidalS2, but I am unable to guess what should be the correct calling parameters. Why MATHEMATICA does not give the right answer, given the fact that the spheroidal functions are supposed to be implemented? Leslaw
POSTED BY: Leslaw Bieniasz

I don't know anything about spheroidal functions, but in the documentation about SpheroidalPS I see that the differential equation

DSolve[(1 - x^2) y''[x] - 
   2 x y'[x] + (SpheroidalEigenva c] + c^2 (1 - x^2) - m^2/(
      1 - x^2)) y[x] == 0, y, x]

in solved in terms of Spheroidal functions. Your first equation is similar to the special case with m=0.
POSTED BY: Gianluca Gorni
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