Glaisher–Kinkelin constant
In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to special functions like the K-function and the Barnes G-function. The constant also appears in a number of sums and integrals, especially those involving the gamma function and the Riemann zeta function. It is named after mathematicians James Whitbread Lee Glaisher and Hermann Kinkelin.
Its approximate value is:
Glaisher's constant plays a role both in mathematics and in physics. It appears when giving a closed form expression for Porter's constant, when estimating the efficiency of the Euclidean algorithm. It also is connected to solutions of Painlevé differential equations and the Gaudin model.