y = x! , Find y′


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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

	$God bless you sir .$
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