OFFSET
1,3
COMMENTS
Cauchy's residue theorem implies that Integral_{x=0..oo} 1/(1 + x^m) dx = (Pi/m) * csc(Pi/m); this is the case m = 5.
The area of a circle circumscribing a unit-area regular decagon.
REFERENCES
Jean-François Pabion, Éléments d'Analyse Complexe, licence de Mathématiques, page 111, Ellipses, 1995.
FORMULA
Equals Integral_{x=0..oo} 1/(1 + x^5) dx.
Equals (Pi/5) *csc(Pi/5).
Equals 1/Product_{k>=1} (1 - 1/(5*k)^2). - Amiram Eldar, Mar 12 2022
EXAMPLE
1.0689593321155951134251843725068826399014509252665...
MAPLE
evalf(4*Pi / (5*(sqrt(10-2sqrt(5)))), 100);
MATHEMATICA
First[RealDigits[N[4Pi/(5Sqrt[10-2Sqrt[5]]), 93]]] (* Stefano Spezia, Mar 12 2022 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Mar 12 2022
STATUS
approved