Glaisher

Glaisher
is Glaisher's constant with numerical value .

DetailsDetails

  • Mathematical constant treated as numeric by NumericQ and as a constant by D.
  • Glaisher can be evaluated to any numerical precision using N.
  • Glaisher's constant A satisfies , where is the Riemann zeta function.

Background
Background

  • Glaisher is the symbol representing Glaisher's constant , also known as the GlaisherKinkelin constant. Glaisher has a number of equivalent definitions throughout mathematics but is most commonly defined as the constant that satisfies , where is the Riemann zeta function Zeta, is its derivative evaluated at , and Log is the natural logarithm. Glaisher has a numerical value . Glaisher arises in mathematical computations including sums, products, and integrals but is especially prominent in sums and integrals involving Gamma and Zeta functions.
  • When Glaisher is used as a symbol, it is propagated as an exact quantity. Expansion and simplification of complicated expressions involving Glaisher may require use of functions such as FunctionExpand and FullSimplify.
  • It is not currently known if Glaisher is rational (meaning it can be expressed as a ratio of integers), algebraic (meaning it is the root of some integer polynomial), or normal (meaning the digits in its base- expansion are equally distributed) to any base.
  • Glaisher can be evaluated to arbitrary numerical precision using N. However, no efficient formulas for computing large numbers of its digits are currently known. RealDigits can be used to return a list of digits of Glaisher and ContinuedFraction to obtain terms of its continued fraction expansion.
Introduced in 1999
(4.0)