Glaisher–Kinkelin constant

The constant of Glaisher - Kinkelin, often only glaishersche constant is a mathematical constant that occurs in some sums and integrals, especially related to the gamma function and the Riemann zeta function. It is named after JWL Glaisher and Hermann Kinkelin.

Approximation

The constant of Glaisher - Kinkelin is commonly referred to. An approximate value is

The individual digits form the sequence A074962 in OEIS.

Definitions

A possible definition of

With the K - function

Another definition is

Which represents a relationship to derive the Riemann zeta function.

A further definition using the circle number is:

With the barnesschen G function

Another possibility with the gamma function is:

A number representation is ( Guillera, Sondow 2008)