Find-all-function-f-R-R-such-that-f-x-1-xf-x-f-0-1-f-x-x-

Question Number 4102 by prakash jain last updated on 28/Dec/15

Find all function f : R \to R

such that

f (x + 1) = x f (x)

f (0) = 1

f (x) \neq Γ (x)

Commented by prakash jain last updated on 28/Dec/15

Γ (x) is gamma function .

Commented by 123456 last updated on 28/Dec/15

i think that if function need to be continuous

then Γ is the only function

Commented by Filup last updated on 29/Dec/15

x = 0

f (0 + 1) = 0 f (0)

∴ f (1) = 0

Γ (1) = 1

∴ f (x) \neq Γ (x) ? ? ?

Commented by 123456 last updated on 29/Dec/15

f (1) = 1 for gamma function

Commented by Filup last updated on 29/Dec/15

but if f (x) = Γ (x)

x = 1

f (1) = 0

Γ (1) = 1

∴ f (x) \neq Γ (x)

I a m c o n f u s e d

Commented by prakash jain last updated on 29/Dec/15

Find f meeting th conditions given above .

Functions other than Γ function .