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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A231535 Decimal expansion of Pi^4/15. 1
6, 4, 9, 3, 9, 3, 9, 4, 0, 2, 2, 6, 6, 8, 2, 9, 1, 4, 9, 0, 9, 6, 0, 2, 2, 1, 7, 9, 2, 4, 7, 0, 0, 7, 4, 1, 6, 6, 4, 8, 5, 0, 5, 7, 1, 1, 5, 1, 2, 3, 6, 1, 4, 4, 6, 0, 9, 7, 8, 5, 7, 2, 9, 2, 6, 6, 4, 7, 2, 3, 6, 9, 7, 1, 2, 1, 8, 1, 3, 0, 7, 9, 3, 4, 1, 4, 5, 7, 8, 1, 5, 6, 5, 0, 1, 9, 9, 5, 0, 3, 3, 9, 7, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Under proper scaling, the radiation distribution density function in terms of frequency is given by prl(x) = x^3/(exp(x)-1), the Planck's radiation law. This constant is the integral of prl(x) from 0 to infinity and leads to the total amount of electromagnetic radiation emitted by a body.

Also, in an 8-dimensional unit-radius hypersphere, equals one-fifth of its surface (A164109), and twice the integral of r^2 over its volume.

Equals 6*zeta(4), see A013662. [Bruno Berselli, Nov 12 2013]

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..1000

S. Sykora, Surface Integrals over n-Dimensional Spheres

S. Sykora, Volume Integrals over n-Dimensional Ellipsoids

Wikipedia, Plank's Law

Ke Xiao, Dimensionless Constants and Blackbody Radiation Laws, Electronic Journal of Theoretical Physics, 8(2011), 379-388, Eq.6.

FORMULA

a = Gamma(4)*zeta(4) = 2*3*product(prime p)(p^4/(p^4-1)). - Stanislav Sykora, Oct 20 2014

EXAMPLE

6.4939394022668291490960221792470074166485057115123614460978572926647...

MATHEMATICA

RealDigits[Pi^4/15, 10, 105][[1]] (* Bruno Berselli, Nov 12 2013 *)

CROSSREFS

Cf. A000796, A013662, A081819, A164109.

Sequence in context: A179258 A248930 A021158 * A019931 A195414 A153630

Adjacent sequences:  A231532 A231533 A231534 * A231536 A231537 A231538

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Nov 12 2013

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 22 20:08 EDT 2017. Contains 286906 sequences.