frobenius

# frobenius - Series Solutions to Linear Ordinary...

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Series Solutions to Linear Ordinary Differential Equations III Method of Frobenius ODE for a 2nd order linear differential equation with a regular singular point ( 29 ( 29 ( 29 ( 29 0 y x q ' y x p x x ' ' y x x 0 2 0 = + - + - This requires p(x) and q(x) are analytic at 0 x x = Method of Frobenius solution. At least one solution is of the form ( 29 ( 29 ( 29 = - - = 0 n n 0 n r 0 x x c x x x y where r is a constant. For 0 x 0 = ODE: ( 29 ( 29 0 y x q ' y x xp ' ' y x 2 = + + Series ( 29 + + + + + = = = + + + + = + = 4 r 4 3 r 3 2 r 2 1 r 1 r 0 0 n r n n 0 n n n r x c x c x c x c x c x c x c x x y Derivatives ( 29 = - + + = 0 n 1 r n n x c r n ' y ( 29 ( 29 ( 29 ( 29 + + + + + + + + + = + + + - 3 r 4 2 r 3 1 r 2 r 1 1 r 0 x c 4 r x c 3 r x c 2 r x c 1 r x rc ( 29 ( 29 = - + - + + = 0 n 2 r n n x c 1 r n r n ' ' y ( 29 ( 29 ( 29 ( 29 r 2 1 r 1 2 r 0 x c 1 r 2 r x c 1 r r x c 1 r r + + + + + - = - - ( 29 ( 29 ( 29 ( 29 + + + + + + + + + 2 r 4 1 r 3 x c 3 r 4

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## This note was uploaded on 04/11/2008 for the course CHNE 525 taught by Professor Prinja during the Fall '08 term at New Mexico.

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frobenius - Series Solutions to Linear Ordinary...

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