Fransén-Robinson constant

The Fransén – Robinson constant , named after Arne Fransén and Herman P. Robinson, is a mathematical constant . It is defined as the area between the reciprocal of the gamma function and the x-axis in the range : ${\displaystyle F}$ ${\displaystyle x>0}$

${\displaystyle F=\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.}$

The decimal expansion of the Fransén – Robinson constant is

F = 2.80777 02420 28519 36522 50118 65577 72932 30808 59209 30198… (follow A058655 in OEIS ),

their continued fraction expansion

[2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 10, 1, 4, 7, 2, 2, 2, 46, 18, 1, 1, 3, 1, 1, 4, 5, 1, 1, …] (Follow A046943 in OEIS ).

literature

• Arne Fransén: Accurate determination of the inverse gamma integral (October 25, 1978). In: B IT Numerical Mathematics , March 19, 1979, pp. 137-138, doi: 10.1007 / BF01931232 (English)
• Arne Fransén, Staffan Wrigge: High-precision values ​​of the gamma function and of some related coefficients . In: Mathematics of Computation , 34, April 1980, pp. 553–566, doi: 10.2307 / 2006104 (English)
• Arne Fransén: Addendum and corrigendum to “High-precision values ​​of the gamma function and of some related coefficients” . In: Mathematics of Computation , 37, July 1981, pp. 233–235, doi: 10.2307 / 2007517 (English)
• Steven R. Finch: Fransén-Robinson constant , Chapter 4.6 in Mathematical constants . Cambridge University Press, Cambridge 2003, ISBN 0-521-81805-2 , pp. 262-264 (English)
• Jonathan Borwein , David Bailey , Roland Girgensohn: Experimentation in mathematics: Computational paths to discovery . AK Peters, Natick 2003, ISBN 1-56881-136-5 . P. 288 (English)

Web links

• Eric W. Weisstein : Fransén – Robinson Constant . In: MathWorld (English).
• Fransen-Robinson constant ( Memento from July 22, 2011 in the Internet Archive ) at Plouffe's Inverter, August 26, 1997 (English)