prove-that-Im-i-1-2-pi-2-coth-pi-m-n-

Question Number 154235 by mnjuly1970 last updated on 15/Sep/21

p r o v e t h a t :

I m (ψ (i)) = \frac{1}{2} + \frac{π}{2} c o t h (π)

m . n

Answered by mindispower last updated on 16/Sep/21

Ψ (1 - i) - Ψ (i) = π c o t (i π) \dots . 1

u s i n g Ψ (1 - x) - Ψ (x) = π c o t (π x)

Ψ (1 + (- i)) = \frac{1}{- i} + Ψ (- i)

I m Ψ (- i) = - I m (Ψ (i))

\Rightarrow I m (Ψ (1 - i)) = 1 - I m (Ψ (i))

1 \Rightarrow - 2 I m (Ψ (i)) + 1 = I m (π c o t (i π))

\Rightarrow I m Ψ (i) = \frac{1}{2} + \frac{π c o t h (π)}{2}

\Rightarrow

Commented by mnjuly1970 last updated on 16/Sep/21

t h a n k s a l o t \dots m r p o w e r

Commented by mindispower last updated on 16/Sep/21

p l e a s u r