GammaEpsilon
GammaEpsilon[exp]
gives a series expansion of Gamma[exp]
in Epsilon
up to order 6
(where EulerGamma
is neglected).
See also
Overview, GammaExpand, Series2.
Examples
If the argument is of the form (1+a Epsilon)
the result is not calculated but tabulated.
GammaEpsilon[1 + a Epsilon]
ε5(−5a5ζ(5)−361π2a5ζ(3))+1601π4a4ε4−31a3ε3ζ(3)+121π2a2ε2+C$16471ε6+1
GammaEpsilon[1 - Epsilon/2]
C$16508ε6+2560π4ε4+48π2ε2+ε5(1152π2ζ(3)+160ζ(5))+24ε3ζ(3)+1
For other arguments the expansion is calculated.
C$17651ε6+160π4ε3+12π2ε+ε1+7201ε5(16861π6+10ψ(2)(1)2)+6ε2ψ(2)(1)+5040ε6(−84π2ζ(5)+421π4ψ(2)(1)+ψ(6)(1))+1201ε4(35π2ψ(2)(1)−24ζ(5))
Γ(x)