Notations C

$\mathbb{C}$: complex plane; Common Notations and Definitions
$\subset$: is contained in; Common Notations and Definitions
$\subseteq$: is, or is contained in; Common Notations and Definitions
$C(\NVar{I})$ or $C(\NVar{a,b})$: continuous on an interval $I$ or $(a,b)$ ; §1.4(ii)
$C\left(\NVar{n}\right)$: Catalan number; (26.5.1)
$c\left(\NVar{n}\right)$: number of compositions of $n$ ; §26.11
$C\left(\NVar{z}\right)$: Fresnel integral; (7.2.7)
$C_{1}(\NVar{z})=C\left(\sqrt{2/\pi}z\right)$: alternative notation for the Fresnel integral; §7.1
(with $C\left(\NVar{z}\right)$ : Fresnel integral and $\pi$ : the ratio of the circumference of a circle to its diameter)
$C_{2}(\NVar{z})=C\left(\sqrt{2z/\pi}\right)$: alternative notation for the Fresnel integral; §7.1
(with $C\left(\NVar{z}\right)$ : Fresnel integral and $\pi$ : the ratio of the circumference of a circle to its diameter)
$c_{\NVar{k}}\left(\NVar{n}\right)$: Ramanujan’s sum; (27.10.4)
$C_{\NVar{\ell}}\left(\NVar{\eta}\right)$: normalizing constant for Coulomb radial functions; (33.2.5)
$c_{\NVar{m}}\left(\NVar{n}\right)$: number of compositions of $n$ into exactly $m$ parts; §26.11
$C_{\NVar{n}}\left(\NVar{x}\right)$: dilated Chebyshev polynomial; (18.1.3)
$\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)$: cylinder function; §10.2(ii)
$C^{\NVar{n}}(\NVar{I})$ or $C^{\NVar{n}}(\NVar{a,b})$: continuously differentiable $n$ times on an interval $I$ or $(a,b)$ ; §1.4(iii)
$C^{\infty}(\NVar{I})$ or $C^{\infty}(\NVar{a,b})$: infinitely differentiable on an interval $I$ or $(a,b)$ ; §1.4(iii)
$C^{(\NVar{\lambda})}_{\NVar{\alpha}}\left(\NVar{z}\right)$: Gegenbauer function; (15.9.15)
$C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)$: ultraspherical (or Gegenbauer) polynomial; Table 18.3.1
$c\left(\NVar{\mathrm{condition}},\NVar{n}\right)$: restricted number of compositions of $n$ ; §26.11
$C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)$: Charlier polynomial; Table 18.19.1
$C_{\NVar{n}}^{\NVar{m}}(\NVar{z},\NVar{\xi})$: Ince polynomials; §28.31(ii)
$c\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)$: irregular Coulomb function; (33.14.9)
$C(\NVar{f},\NVar{h})(\NVar{x})$: cardinal function; (3.3.43)
$C_{\NVar{n}}\left(\NVar{x};\NVar{\beta}\,|\,\NVar{q}\right)$: continuous $q$ -ultraspherical polynomial; (18.28.13)
$\operatorname{cd}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.8)
$\mathit{cdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z},\NVar{k^{2}}\right)$: Lamé polynomial; (29.12.7)

$\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$: Mathieu function; §28.2(vi)
$\operatorname{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$: modified Mathieu function; (28.20.3)
$\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z},\NVar{k^{2}}\right)$: Lamé polynomial; (29.12.3)
$\operatorname{ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$: Mathieu function of noninteger order; (28.12.12)
$\mathrm{ceh}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{Ce}_{n}\left(z,q\right)$: notation used by Campbell (1955); §28.1
(with $\operatorname{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$ : modified Mathieu function)
$\operatorname{cel}\left(\NVar{k_{c}},\NVar{p},\NVar{a},\NVar{b}\right)$: Bulirsch’s complete elliptic integral; (19.2.11)
$\chi\left(\NVar{n}\right)$: Dirichlet character; §27.8
$\chi(\NVar{x})$: ratio of gamma functions; §9.7(i)
$\operatorname{Chi}\left(\NVar{z}\right)$: hyperbolic cosine integral; (6.2.16)
$\operatorname{Ci}\left(\NVar{z}\right)$: cosine integral; (6.2.11)
$\operatorname{Ci}\left(\NVar{a},\NVar{z}\right)$: generalized cosine integral; (8.21.2)
$\operatorname{ci}\left(\NVar{a},\NVar{z}\right)$: generalized cosine integral; (8.21.1)
$\operatorname{Cin}\left(\NVar{z}\right)$: cosine integral; (6.2.12)
$\operatorname{cn}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.5)
$\mathrm{cn}(\NVar{z}\mathpunct{|}\NVar{m})=\operatorname{cn}\left(z,\sqrt{m}\right)$: alternative notation; §22.1
(with $\operatorname{cn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function)
$\cos\NVar{z}$: cosine function; (4.14.2)
$\operatorname{Cos}_{\NVar{q}}\left(\NVar{x}\right)$: $q$ -cosine function; (17.3.6)
$\operatorname{cos}_{\NVar{q}}\left(\NVar{x}\right)$: $q$ -cosine function; (17.3.5)
$\cosh\NVar{z}$: hyperbolic cosine function; (4.28.2)
$\cot\NVar{z}$: cotangent function; (4.14.7)
$\coth\NVar{z}$: hyperbolic cotangent function; (4.28.7)
$\operatorname{cs}\left(\NVar{z},\NVar{k}\right)$: Jacobian elliptic function; (22.2.9)
$\csc\NVar{z}$: cosecant function; (4.14.5)
$\operatorname{csch}\NVar{z}$: hyperbolic cosecant function; (4.28.5)
$\operatorname{curl}$: of vector-valued function; (1.6.22)

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