login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202623 Decimal expansion of (1/3)! = Gamma(4/3). 3
8, 9, 2, 9, 7, 9, 5, 1, 1, 5, 6, 9, 2, 4, 9, 2, 1, 1, 2, 1, 8, 5, 6, 4, 3, 1, 3, 6, 5, 8, 2, 2, 5, 8, 8, 1, 3, 7, 6, 2, 2, 9, 7, 9, 2, 6, 5, 2, 4, 3, 3, 7, 0, 0, 3, 1, 6, 8, 0, 9, 4, 4, 2, 5, 3, 0, 1, 3, 9, 2, 0, 3, 3, 8, 9, 2, 4, 7, 9, 3, 9, 8, 4, 6, 9, 9, 4, 2, 9, 6, 3, 4, 7, 0, 6, 2, 9, 2, 9, 8, 0, 6, 3, 8, 6, 3, 4, 9, 7, 3, 3, 3, 5, 7, 4, 2, 1, 1, 1, 1, 9, 0, 6, 3, 6, 1, 5, 2, 3, 1, 6, 8, 1, 5, 7, 4, 1, 9, 9, 9, 2, 5, 7, 1, 1, 2, 2, 5, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..149.

Index to sequences related to the Gamma function

FORMULA

A formula from R. W. Gosper, Posting to Math Fun Mailing List, Dec 27 2011: (Start)

Gamma[1/3] == (2*2^(7/9)*((Pi*EllipticTheta[3, 0, E^(-((16*Pi)/Sqrt[3]))])/

             (1 + 1/(2^(1/4)*Sqrt[1 + Sqrt[3]]) +

                (2^(7/16)*((-1 + Sqrt[2])/(-Sqrt[2] + Sqrt[3]))^(1/4))/(-1

+

             Sqrt[3])^(1/8)))^

          (2/3))/3^(1/4)

Macsyma:  GAMMA(1/3) =

4^(8/9)*%PI^(2/3)*THETA[3](0,%E^-(16*%PI/SQRT(3)))^(2/3)/(3^(1/4)*(2^(7/16)*(SQRT(2)-1)^(1/4)/((SQRT(3)-1)^(1/8)*(SQRT(3)-SQRT(2))^(1/4))+1/(2^(1/4)*SQRT(SQRT(3)+1))+1)^(2/3))

This is exact, but degrades to 50+ digits if you replace

THETA[3](0,%E^-(16*%PI/SQRT(3)))

by 1+2*%E^-(16*%PI/SQRT(3)). (End)

Also equals integral_{0..oo} exp(-x^3) dx [Jean-Fran├žois Alcover, Mar 29 2013]

EXAMPLE

.89297951156924921121856431365822588137622979265243370031680...

MAPLE

evalf(GAMMA(4/3)) ;

MATHEMATICA

RealDigits[(1/3)!, 10, 150][[1]] (* or *) RealDigits[Gamma[4/3], 10, 150] [[1]] (* Harvey P. Dale, Sep 03 2016 *)

CROSSREFS

Cf. A068467.

Sequence in context: A201406 A242972 A198142 * A266261 A117914 A203077

Adjacent sequences:  A202620 A202621 A202622 * A202624 A202625 A202626

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Dec 29 2011

EXTENSIONS

Corrected and extended by Harvey P. Dale, Sep 03 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)