
JeanneDArcAlter
Crushing loneliness
- Joined
- Nov 6, 2024
- Posts
- 23,925
- Reputation
- 37,927
tan^cos(x^y)(x^y) = (π/2)^(i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (4^s (x^y)^(-2 s) Γ(s))/Γ(1/2 - s) ds) ( integral_0^∞ (-1 + t^((2 x^y)/π))/(-1 + t^2) dt)^(-i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (4^s (x^y)^(-2 s) Γ(s))/Γ(1/2 - s) ds) for (0<γ<1/2 and x^y>0 and 0<Re(x^y)<π/2)
tan^cos(x^y)(x^y) = 8^( sum_(k=0)^∞ ((-1)^k (x^y)^(2 k))/(2 k)!) (x^y sum_(k=1)^∞ 1/((1 - 2 k)^2 π^2 - 4 x^(2 y)))^( sum_(k=0)^∞ ((-1)^k (x^y)^(2 k))/(2 k)!) for -1/2 + x^y/π not element Z