conductor

SearchAdvancedHelp

(0.001 seconds)

2 matching pages

1: 24.16 Generalizations

… ►

§24.16(ii) Character Analogs

… ►Then $f$ is called the conductor of $\chi$. Generalized Bernoulli numbers and polynomials belonging to $\chi$ are defined by ►

24.16.10 $$\sum _{a=1}^f\frac{\chi (a)t{\mathrm{e}}^{at}}{{\mathrm{e}}^{ft}-1}=\sum _{n=0}^{\mathrm{\infty }}{B}_{n,\chi }\frac{t^n}{n!},$$

ⓘ

Symbols:

$\mathrm{e}$: base of natural logarithm, $!$: factorial (as in $n!$), $n$: integer, $t$: real or complex, $\chi (a)$: Dirichlet character, $f$: conductor and $B_{n,\chi }$: Generalized Bernoulli numbers

Permalink:

http://dlmf.nist.gov/24.16.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §24.16(ii), §24.16 and Ch.24

…

2: 10.73 Physical Applications

… ►The analysis of the current distribution in circular conductors leads to the Kelvin functions $\mathrm{ber}x$, $\mathrm{bei}x$, $\ker x$, and $\mathrm{kei}x$. …