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hypergeometric equation (Definition)

The hypergeometric equation is the following linear ordinary differential equation:

$\displaystyle x (1 - x) y'' + (c - (a + b + 1) x ) y' + aby = 0$
(Here, $ a$, $ b$, and $ c$ are complex constants.)

The solutions of this equation may be expressed in terms of the hypergeometric function, hence the name.

The hypergeometric equation is a Fuchsian differential equation with singularities at 0, $ 1$, and $ \infty$. By a suitable change of variables, any second order Fuchsian differential equation may be converted into a hypergeometric equation.



"hypergeometric equation" is owned by rspuzio.
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Cross-references: second order, variables, Fuchsian differential equation, hypergeometric function, terms, equation, solutions, complex, linear ordinary differential equation
There are 3 references to this entry.

This is version 2 of hypergeometric equation, born on 2004-10-24, modified 2005-05-07.
Object id is 6409, canonical name is HypergeometricEquation.
Accessed 3384 times total.

Classification:
AMS MSC: 33C05 (Special functions :: Hypergeometric functions :: Classical hypergeometric functions, $_2F_1$)
Pending Errata and Addenda
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