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3 votes

Generalized Fuchsian-type PDE?

Here's one way to get the hypergeometric function for the "simpler" equation: Consider the operator $x^3 (1 + t\partial_t)(\partial^3_{xxx} + \frac{6}x \partial^2_{xx} + \frac{6}{x^2} \...
Willie Wong's user avatar
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5 votes

Generalized Fuchsian-type PDE?

In your simplified case, I don't see how $A(x,0) = 1$. In fact, the overall factor of $t$ should for the solution to vanish for all $x$ at $t=0$. Actually, I think there is no solution to your ...
Igor Khavkine's user avatar
3 votes

Generalized Fuchsian-type PDE?

Non really an answer but a long comment with some (hopefully useful) suggestions. The equation you are studying seems tractable by using the method of multidimensional Mellin transform described by ...
Daniele Tampieri's user avatar

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