By-the-use-of-substitution-x-2-show-that-the-legendary-equation-1-2-y-2-y-n-n-1-y-0-where-n-is-a-constant-change-to-hyper-geometric-equation-hence-obtain-the-solution-to-

Question Number 7628 by Tawakalitu. last updated on 06/Sep/16

B y t h e u s e o f s u b s t i t u t i o n x = μ^{2}, s h o w t h a t

t h e l e g e n d a r y e q u a t i o n,

(1 - μ^{2}) y^{″} - 2 μ y^{'} + n (n + 1) y = 0,

w h e r e n i s a c o n s t a n t c h a n g e t o h y p e r g e o m e t r i c

e q u a t i o n . h e n c e o b t a i n t h e s o l u t i o n t o t h e

r e s u l t i n g h y p e r g e o m e t r i c d i f f e r e n t i a l e q u a t i o n

b y w a y o f c o m p a r i s o n .