Fransén-Robinson Constant

Author

Eric W. Weisstein
January 27, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Fransen-RobinsonConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Fransen-RobinsonConstant.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Constant

FunctionExpand[1/Gamma[x],x>0]

Integrate[1/Gamma[x],x]

Integrate[1/Gamma[x],{x,0,x}]

Integrate[1/Gamma[x],{x,0,Infinity}]

NIntegrate[1/Gamma[x],{x,0,Infinity},WorkingPrecision->30]

Series

Series[1/Gamma[x],{x,0,5}]//Simplify

SeriesCoefficient[1/Gamma[x],{x,0,n}]

Series[1/Gamma[x],{x,∞,3}]

SeriesCoefficient[1/Gamma[x],{x,∞,n}]

Plot

Integrate[1/Gamma[t],{t,0,x}]//TraditionalForm

MakeBoxes[ordinate,TraditionalForm]:=RowBox[{SubsuperscriptBox["∫","0","x"],RowBox[{FractionBox[RowBox[{"d"," ","t"}],RowBox[{"Γ","(","t",")"}]]}]}]

Show[GraphicsArray[Block[{$DisplayFunction=Identity},
{
Plot[1/Gamma[x],{x,0,10},PlotStyle->Red,
AxesLabel->TraditionalForm/@{x,1/Gamma[x]}],
Plot[Integrate[1/Gamma[t],{t,0,x}],{x,0,10},PlotStyle->Red,
AxesLabel->TraditionalForm/@{x,ordinate}]
}],
GraphicsSpacing->-.1]
]