A257957 Decimal expansion of log(Gamma(1/Pi)).

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

Offset

1,3

Comments

The reference gives an interesting series representation with rational coefficients for log(Gamma(1/Pi)) = (1-1/Pi)*log(Pi) - 1/Pi + log(2)/2 + (1 + 1/4 + 1/12 + 1/32 + 1/75 + 1/144 + 13/2880 + 157/46080 + ...)/(2*Pi).

The value log(Gamma(1/Pi)) is also intimately related to integral_{x=0..1} arctan(arctanh(x))/x (A257963).

Links

Table of n, a(n) for n=1..103.

Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to 1/Pi, Mathematics of Computation (AMS), 2015.

Example

1.0336461257655827064855374553316178667100308701595988...

Maple

evalf(log(GAMMA(1/Pi)), 120);

Mathematica

RealDigits[Log[Gamma[1/Pi]], 10, 120][[1]]

Prog

(PARI) default(realprecision, 120); log(gamma(1/Pi))

Crossrefs

Cf. A257955, A257963, A257958, A257959, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.

Sequence in context: A372036 A143305 A051472 * A369501 A324000 A048149

Adjacent sequences: A257954 A257955 A257956 * A257958 A257959 A257960

Keyword

nonn,cons

Author

Iaroslav V. Blagouchine, May 14 2015

Status

approved