Notations B

$b_{\NVar{k}}$: $k$ th zero of Airy $\operatorname{Bi}$ ; §9.9(i)
$b^{\prime}_{\NVar{k}}$: $k$ th zero of Airy $\operatorname{Bi}'$ ; §9.9(i)
$B_{\NVar{n}}$: Bernoulli numbers; §24.2(i)
$B_{\NVar{n-k}}^{(-\NVar{k})}=S\left(n,k\right)/\genfrac{(}{)}{0.0pt}{}{n}{k}$: notation used by Milne-Thomson (1933); §26.1
(with $S\left(\NVar{n},\NVar{k}\right)$ : Stirling number of the second kind and $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$ : binomial coefficient)
$B^{(\NVar{\ell})}_{\NVar{n}}$: generalized Bernoulli numbers; §24.16(i)
$B_{\NVar{n-k}}^{(\NVar{n})}=s\left(n,k\right)/\genfrac{(}{)}{0.0pt}{}{n-1}{k-1}$: notation used by Milne-Thomson (1933); §26.1
(with $s\left(\NVar{n},\NVar{k}\right)$ : Stirling number of the first kind and $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$ : binomial coefficient)
$B^{(\NVar{x})}_{\NVar{n}}$: Nörlund polynomials; §24.16(i)
$B\left(\NVar{n}\right)$: Bell number; §26.7(i)
$b_{\NVar{n}}\left(\NVar{q}\right)$: eigenvalues of Mathieu equation; §28.2(v)
$B_{\NVar{n}}\left(\NVar{x}\right)$: Bernoulli polynomials; §24.2(i)
$B_{\NVar{n}}\left(\NVar{z}\right)$: generalized Airy function; §9.13(i)
$B_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)$: Bessel function of matrix argument (second kind); (35.5.3)
$B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)$: generalized Bernoulli polynomials; §24.16(i)
$\widetilde{B}_{\NVar{n}}\left(\NVar{x}\right)$: periodic Bernoulli functions; §24.2(iii)

$b^{\NVar{n}}_{\NVar{\nu}}\left(\NVar{k^{2}}\right)$: eigenvalues of Lamé’s equation; §29.3(i)
$\mathrm{B}\left(\NVar{a},\NVar{b}\right)$: beta function; (5.12.1)
$B_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)$: generalized Airy function; §9.13(ii)
$\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right)$: multivariate beta function; (35.3.3)
$\mathrm{B}_{\NVar{q}}\left(\NVar{a},\NVar{b}\right)$: $q$ -beta function; (5.18.11)
$\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)$: incomplete beta function; (8.17.1)
$B(\NVar{a},\NVar{b},\NVar{x})=\mathrm{B}_{x}\left(a,b\right)$: notation used by Magnus et al. (1966); §8.1
(with $\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)$ : incomplete beta function)
$\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)$: Kelvin function; (10.61.1)
$\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)$: Kelvin function; (10.61.1)
$\beta_{\NVar{k}}$: $k$ th complex zero of Airy $\operatorname{Bi}$ ; §9.9(i)
$\beta^{\prime}_{\NVar{k}}$: $k$ th complex zero of Airy $\operatorname{Bi}'$ ; §9.9(i)
$\beta_{\NVar{n}}\left(\NVar{x},\NVar{q}\right)$: $q$ -Bernoulli polynomial; (17.3.7)
$\operatorname{Bi}\left(\NVar{z}\right)$: Airy function; §9.2(i)