Glaisher¶

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description¶

Glaisher
    is the Glaisher-Kinkelin constant A, with numerical value ~= 1.28243.
Glaisher's constant satisfies Log[A] == 1/12 - Zeta'[-1], where Zeta is
the Riemann zeta function. It is a mathematical constant: it has
attributes Constant and Protected, NumericQ[Glaisher] is True, and
D[Glaisher, x] is 0. N[Glaisher, prec] evaluates it to any precision.

Examples¶

No verified examples yet for this function.

Implementation notes¶

Attributes Constant, Protected. `Attributes[Glaisher] = {Constant,

Attributes: Constant, Protected.

Implementation status¶

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References¶

Source: src/info.c
Specification: docs/spec/builtins/mathematical-constants.md

Notes & additional examples¶

Worked examples¶

In[1]:= N[Glaisher]
Out[1]= 1.28243

In[1]:= N[Glaisher, 40]
Out[1]= 1.2824271291006226368753425688697917277676

In[1]:= NumericQ[Glaisher]
Out[1]= True

In[1]:= D[Glaisher, x]
Out[1]= 0

Notes¶

Glaisher is the Glaisher-Kinkelin constant A, defined by Log[A] == 1/12 - Zeta'[-1] and appearing in the asymptotics of the hyperfactorial and in many Zeta-derivative identities. It is held symbolic (attributes Constant and Protected, so D[Glaisher, x] is 0 and NumericQ is True) until N forces a value; N[Glaisher, 40] returns it to 40 digits via its MPFR series.