This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# StieltjesGamma

 StieltjesGamma[n]gives the Stieltjes constant . StieltjesGammagives the generalized Stieltjes constant .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• is the coefficient of in the Laurent expansion of about the point .
• The are generalizations of Euler's constant; .
• is the coefficient of in the Laurent expansion of about the point .
• For certain special arguments, StieltjesGamma automatically evaluates to exact values.
Evaluate to high precision:
Plot values of StieltjesGamma:
Evaluate to high precision:
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Plot values of StieltjesGamma:
 Out[1]=

 Out[1]=
 Scope   (4)
Evaluate for complex second argument:
The precision of the output tracks the precision of the input:
 Applications   (3)
Expansion of the Riemann zeta function:
Expansion of the Hurwitz zeta function:
Test Li's criterion for the Riemann hypothesis:
All values should be positive:
Express integrals in terms of StieltjesGamma:
The EulerGamma case evaluates automatically:
Various symbolic relations are automatically used:
Substitution of derivatives of Zeta at yields indeterminate values:
Use Limit to obtain the expansion coefficient:
The argument of StieltjesGamma must be an exact non-negative integer:
Use N to obtain a numerical approximation:
Alternatively, use two-argument form:
StieltjesGamma does not allow numericalization of its index:
It is currently not known if Stieltjes constants are algebraic numbers: