y-x-Find-y-

Question Number 17634 by tawa tawa last updated on 08/Jul/17

y = x!, Find y^{'}

Answered by alex041103 last updated on 09/Jul/17

B e c a u s e x! i s d e f i n e d o n l y f o r n o n - n e g a t i v e

i n t e g e r s, i . e . t h e f u n c t i o n {i s n}^{'} t c o n t i n i o u s

w e c a n n o t i n t a g r a t e o r d i f e r e n t i a t e i t .

T h e r e i s a n a n a l i t i c c o n t i n u a t i o n

o f t h e f a c t o r i a l f u n c t i o n c a l l e d t h e

G a m m a f u n c t i o n

x! = Γ (x + 1) = \underset{0}{\int^{\infty}} t^{x} e^{- t} d t

Y o u c a n s e a r c h f o r t h e d e r i v i t i v e o f

t h e g a m m a f u n c t i o n .

Commented by tawa tawa last updated on 09/Jul/17

God bless you sir .