A220086 Decimal expansion of Gamma(1/7).

6, 5, 4, 8, 0, 6, 2, 9, 4, 0, 2, 4, 7, 8, 2, 4, 4, 3, 7, 7, 1, 4, 0, 9, 3, 3, 4, 9, 4, 2, 8, 9, 9, 6, 2, 6, 2, 6, 2, 1, 1, 3, 5, 1, 8, 7, 3, 8, 4, 1, 3, 5, 1, 4, 8, 9, 4, 0, 1, 6, 8, 8, 1, 9, 1, 4, 8, 5, 7, 6, 2, 0, 4, 7, 3, 8, 2, 3, 9, 1, 3, 7, 7, 9, 0, 5, 6

Offset: 1

Author

Bruno Berselli, Dec 12 2012

Keywords

• nonn
• cons

Comments

(A220086/A220605)*(A220607/A220606) = A160389, which is the case n=7 of (Gamma(1/n)/Gamma(2/n))*(Gamma((n-1)/n)/Gamma((n-2)/n)) = 2*cos(Pi/n).

A220086*A220605*A220606*A220607*A220608*A220609 = (2*Pi)^3/sqrt(7), which is the case n=7 of product(Gamma(i/n), i=1..n-1) = sqrt((2*Pi)^(n-1)/n) (see also the second link to Wikipedia).

Continued fraction expansion: 6, 1, 1, 4, 1, 2, 2, 1, 5, 1, 10, 7, 1,...

Examples

			6.5480629402478244377140933494289962626211351873841351...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Wikipedia, Particular values of the Gamma function: General rational arguments
• Wikipedia, Particular values of the Gamma function: Products
• Index to sequences related to the Gamma function

Programs

Magma

SetDefaultRealField(RealField(100)); Gamma(1/7); // G. C. Greubel, Mar 10 2018

Mathematica

RealDigits[Gamma[1/7], 10, 90][[1]]

Maxima

fpprec:90; ev(bfloat(gamma(1/7)));

PARI

default(realprecision, 100); gamma(1/7) \\ G. C. Greubel, Mar 10 2018

Formula

Equals Pi * csc(Pi/7) / A220607, where csc is the cosecant function.

(A220086/A220605) * (A220607/A220606) = A160389, which is the case n=7 of (Gamma(1/n)/Gamma(2/n))*(Gamma((n-1)/n)/Gamma((n-2)/n)) = 2*cos(Pi/n).

A220086*A220605*A220606*A220607*A220608*A220609 = (2*Pi)^3/sqrt(7), which is the case n=7 of product(Gamma(i/n), i=1..n-1) = sqrt((2*Pi)^(n-1)/n) (see also the second link to Wikipedia).

A220086*A220607 = A220605*A220606 + A220608*A220609. - Andrea Pinos, May 21 2025