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A302258
Decimal expansion of the second radiation constant c_2 in meter-kelvin.
0
1, 4, 3, 8, 7, 7, 6, 8, 7, 7, 5, 0, 3, 9, 3, 3, 8, 0, 2, 1, 4, 6, 6, 7, 1, 6, 0, 1, 5, 4, 3, 9, 1, 1, 5, 9, 5, 1, 9, 9, 0, 6, 9, 4, 2, 3, 1, 4, 8, 0, 9, 9, 1, 9, 1, 0, 3, 2, 6, 2, 3, 0, 6, 3, 5, 0, 1, 2, 9, 5, 4, 0, 5, 2, 7, 6, 7, 9, 3, 7, 3, 9, 7, 5, 5, 7, 2
OFFSET
-1,2
COMMENTS
Appears as a term in the Sakuma-Hattori equation for the electromagnetic signal from the thermal radiation emitted by an ideal black body of a given temperature.
It also appears in Planck's law when expressed in terms of the wavenumber. - Charles R Greathouse IV, Jun 25 2021
The exact value, following the 2019 redefinition of SI units, is 272115870842319/18913000000000000. Hence, periodic with period 18912. - Charles R Greathouse IV, Jun 25 2021
In natural (Planck) units this is 2*Pi = A019692. - Charles R Greathouse IV, Jul 07 2021
FORMULA
c_2 = h*c/k where k is Planck's constant, c is the speed of light in a vacuum, and k is the Boltzmann constant. - Charles R Greathouse IV, Jun 25 2021
EXAMPLE
0.014387768775039338021466716015439115951990694231480991910326230635012954... m K.
PROG
(PARI) period(r, base=10)=
{
my(d=denominator(r), f=factor(base)[, 1]);
for(i=1, #f,
d /= f[i]^valuation(d, f[i])
);
znorder(Mod(base, d));
}
rationalNumberOrder(r, base=10)=
{
my(f=factor(base)[, 1], t, L, x='x, P);
for(i=1, #f,
t=valuation(r, f[i]);
if(t<0, r*=f[i]^-t)
);
r = frac(r);
L = period(r, base);
P = Polrev(digits(r*(base^L-1)));
poldegree(denominator(P/(1-x^L)));
}
rationalNumberOrder(272115870842319/18913000000000000) \\ Kevin Ryde and Charles R Greathouse IV, Jul 05 2021
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Felix Fröhlich, Apr 12 2018
EXTENSIONS
More terms from Charles R Greathouse IV, Jun 25 2021
STATUS
approved