A068465 Decimal expansion of Gamma(3/4).

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

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• cons
• easy
• nonn

Examples

			Gamma(3/4) = 1.225416702465177645129098303362890526851239248108070611...
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 43, equation 43:4:14 at page 414.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..20000
• Russell J. Matheson, GAMMA(3/4) computed to 14550 digits.
• Simon Plouffe, GAMMA(3/4) to 256 places, see p. 65.
• Index to sequences related to the Gamma function

Crossrefs

Cf. A000796, A002193, A053004, A063448, A068466, A069998.

Programs

Magma

SetDefaultRealField(RealField(105)); Gamma(3/4); // G. C. Greubel, Mar 11 2018

Maple

evalf(GAMMA(3/4)) ; # R. J. Mathar, Jan 10 2013

Mathematica

RealDigits[Gamma[3/4], 10, 100][[1]] (* G. C. Greubel, Mar 11 2018 *)

PARI

default(realprecision, 100); gamma(3/4) \\ G. C. Greubel, Mar 11 2018

Formula

Gamma(3/4) * A068466 = sqrt(2)*Pi = A063448. - R. J. Mathar, Jun 18 2006

Equals Integral_{x>=0} x^(-1/4)*exp(-x) dx. - Vaclav Kotesovec, Nov 12 2020

Equals (Pi/2)^(1/4) * sqrt(AGM(1,sqrt(2))) = sqrt(A069998 * A053004). - Amiram Eldar, Jun 12 2021