Triangular exponentation logarithm and inverse

66 Views Asked by At

The generalized formula of triangular exponentiation on real numbers field is

$x ^ {\triangle y} = \frac {1} {y \cdot B (x, y)} = \frac {\Gamma(x + y)} {\Gamma(x) \cdot \Gamma(y + 1)} $

It's my assumption of generalization of formula in wikipedia.

How to find the logarithm and inverse exponentiation functions? Is it possible to infer x and y through the (y, n) and (x, n) respectively?

$\frac {\Gamma(x + y)} {\Gamma(x) \cdot \Gamma(y + 1)} = a $