DLMF: Notations B

Notations B

♦*♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

$\mathop{B_{{n}}\/}\nolimits$: Bernoulli numbers; §24.2(i)
$\mathop{b_{{k}}\/}\nolimits$: $k$ th zero of Airy $\mathop{\mathrm{Bi}\/}\nolimits$ ; §9.9(i)
$\mathop{b^{{\prime}}_{{k}}\/}\nolimits$: $k$ th zero of Airy ${\mathop{\mathrm{Bi}\/}\nolimits^{{\prime}}}$ ; §9.9(i)
$\mathop{B^{{(\ell)}}_{{n}}\/}\nolimits$: generalized Bernoulli numbers; ¶ ‣ §24.16(i)
$B_{{n-k}}^{{(n)}}=\mathop{s\/}\nolimits\!\left(n,k\right)/\binom{n-1}{k-1}$: notation used by Milne-Thomson (1933); ¶ ‣ §26.1
(with $\mathop{s\/}\nolimits\!\left(n,k\right)$ : Stirling number of the first kind and $\binom{m}{n}$ : binomial coefficient)
$B_{{n-k}}^{{(-k)}}=\mathop{S\/}\nolimits\!\left(n,k\right)/\binom{n}{k}$: notation used by Milne-Thomson (1933); ¶ ‣ §26.1
(with $\mathop{S\/}\nolimits\!\left(n,k\right)$ : Stirling number of the second kind and $\binom{m}{n}$ : binomial coefficient)
$\mathop{B^{{(x)}}_{{n}}\/}\nolimits$: Nörlund polynomials; ¶ ‣ §24.16(i)
$\mathop{B\/}\nolimits\!\left(n\right)$: Bell number; §26.7(i)
$\mathop{B_{{n}}\/}\nolimits\!\left(x\right)$: Bernoulli polynomials; §24.2(i)
$\mathop{B_{{\nu}}\/}\nolimits\!\left(\mathbf{T}\right)$: Bessel function of matrix argument (second kind); (35.5.3)
$\mathop{B_{{n}}\/}\nolimits\!\left(z\right)$: generalized Airy function; §9.13(i)
$\mathop{b_{{n}}\/}\nolimits\!\left(q\right)$: eigenvalues of Mathieu equation; §28.2(v)
$\mathop{\widetilde{B}_{{n}}\/}\nolimits\!\left(x\right)$: periodic Bernoulli functions; §24.2(iii)
$\mathop{B_{{k}}\/}\nolimits\!\left(z,p\right)$: generalized Airy function; §9.13(ii)

$\mathop{B^{{(\ell)}}_{{n}}\/}\nolimits\!\left(x\right)$: generalized Bernoulli polynomials; ¶ ‣ §24.16(i)
$\mathop{b^{{n}}_{{\nu}}\/}\nolimits\!\left(k^{2}\right)$: eigenvalues of Lamé’s equation; §29.3(i)
$\mathop{\mathrm{B}\/}\nolimits\!\left(a,b\right)$: beta function; (5.12.1)
$\mathop{\mathrm{B}_{{m}}\/}\nolimits\!\left(a,b\right)$: multivariate beta function; (35.3.3)
$\mathop{\mathrm{B}_{{x}}\/}\nolimits\!\left(a,b\right)$: incomplete beta function; (8.17.1)
$\mathop{\mathrm{B}_{{q}}\/}\nolimits\!\left(a,b\right)$: $q$ -beta function; (5.18.11)
$B(a,b,x)=\mathop{\mathrm{B}_{{x}}\/}\nolimits\!\left(a,b\right)$: notation used by Magnus et al. (1966); §8.1
(with $\mathop{\mathrm{B}_{{x}}\/}\nolimits\!\left(a,b\right)$ : incomplete beta function)
$\mathop{\mathrm{bei}_{{\nu}}\/}\nolimits\!\left(x\right)$: Kelvin function; (10.61.1)
$\mathop{\mathrm{ber}_{{\nu}}\/}\nolimits\!\left(x\right)$: Kelvin function; (10.61.1)
$\mathop{\beta _{{k}}\/}\nolimits$: $k$ th complex zero of Airy $\mathop{\mathrm{Bi}\/}\nolimits$ ; §9.9(i)
$\mathop{\beta^{{\prime}}_{{k}}\/}\nolimits$: $k$ th complex zero of Airy ${\mathop{\mathrm{Bi}\/}\nolimits^{{\prime}}}$ ; §9.9(i)
$\mathop{\beta _{{n}}\/}\nolimits\!\left(x,q\right)$: $q$ -Bernoulli polynomial; (17.3.7)
$\mathop{\mathrm{Bi}\/}\nolimits\!\left(z\right)$: Airy function; §9.2(i)