A073006 - OEIS

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A073006

Decimal expansion of Gamma(2/3).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This constant is transcendental: Chudnovsky famously proved that Gamma(1/3) is algebraically independent of Pi, but Gamma(1/3)*Gamma(2/3) = 2*Pi/sqrt(3) by the reflection formula. - Charles R Greathouse IV, Aug 21 2023

REFERENCES

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 43, equation 43:4:8 at page 413.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..5000

Simon Plouffe, GAMMA(2/3).

Index to sequences related to the Gamma function.

Index entries for transcendental numbers.

FORMULA

Gamma(2/3) * A073005 = A186706. - R. J. Mathar, Jun 18 2006

EXAMPLE

1.354117939426400416945288028154513785519327266056793698394022467963782...

MATHEMATICA

RealDigits[ N[ Gamma[2/3], 110]][[1]]

PROG

(PARI) allocatemem(932245000); default(realprecision, 5080); x=gamma(2/3); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b073006.txt", n, " ", d)); \\ Harry J. Smith, May 14 2009

(Magma) SetDefaultRealField(RealField(100)); Gamma(2/3); // G. C. Greubel, Mar 10 2018

CROSSREFS

Cf. A030652 (continued fraction). - Harry J. Smith, May 14 2009

Cf. A073005, A186706.

Sequence in context: A016611 A198619 A168223 * A320029 A317190 A317191

Adjacent sequences: A073003 A073004 A073005 * A073007 A073008 A073009

KEYWORD

cons,nonn,changed

AUTHOR

Robert G. Wilson v, Aug 03 2002

STATUS

approved

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