1-1-6-1-5-6-10-1-1-3-20-3-pi-2-

Question Number 156086 by MathSh last updated on 07/Oct/21

ψ^{(1)} (\frac{1}{6}) - ψ^{(1)} (\frac{5}{6}) = 10 ψ^{(1)} (\frac{1}{3}) - \frac{20}{3} π^{2}

Commented by puissant last updated on 09/Oct/21

ψ^{(1)} (\frac{1}{6}) - ψ^{(1)} (\frac{5}{6}) = π^{2} (1 + {c o t a n}^{2} (\frac{π}{6}))

= π^{2} + π^{2} {c o t a n}^{2} (\frac{π}{6})

{t a n}^{2} (\frac{π}{6}) = \frac{{s i n}^{2} \frac{π}{6}}{{c o s}^{2} \frac{π}{6}} = \frac{1}{4} \times \frac{4}{3} = \frac{1}{3}

\Rightarrow π^{2} + π^{2} {c o t a n}^{2} \frac{π}{6} = π^{2} (1 + \frac{1}{3}) = \frac{4 π^{2}}{3} \dots

Commented by tabata last updated on 08/Oct/21

s i r w h a t s t h e m e a n ψ a n d w h a y s t h e f o r m o l l a ?

Commented by MathSh last updated on 08/Oct/21

Thankyou ser, first formula is wrong

Commented by puissant last updated on 12/Oct/21

M r t a b a t a w e h a v e :

ψ^{(1)} (x) - ψ^{(1)} (1 - x) = π^{2} (1 + {c o t a n}^{2} (π x))