In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function. The constant appears in a number of sums and integrals, especially those involving Gamma functions and zeta functions. It is named after mathematicians James Whitbread Lee Glaisher and Hermann Kinkelin.
Its approximate value is:
The Glaisher–Kinkelin constant can be given by the limit:
The Glaisher–Kinkelin constant also appears in the Riemann zeta function, such as:
where is the Euler–Mascheroni constant.
Some integrals involve this constant:
A series representation for this constant follows from a series for the Riemann zeta function given by Helmut Hasse.
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- Weisstein, Eric W., "Glaisher–Kinkelin Constant", MathWorld.
- Weisstein, Eric W., "Riemann Zeta Function", MathWorld.