# Notations C

*AB♦C♦DEFGHIJKLMNOPQRSTUVWXYZ
$\mathbb{C}$
complex plane; Common Notations and Definitions
$\subset$
is contained in; Common Notations and Definitions
$\subseteq$
is, or is contained in; Common Notations and Definitions
$\mathop{C\/}\nolimits(\NVar{I})$ or $\mathop{C\/}\nolimits(\NVar{a,b})$
continuous on an interval $I$ or $(a,b)$; §1.4(ii)
$\mathop{C\/}\nolimits\!\left(\NVar{n}\right)$
Catalan number; 26.5.1
$\mathop{c\/}\nolimits\!\left(\NVar{n}\right)$
number of compositions of $n$; §26.11
$\mathop{C\/}\nolimits\!\left(\NVar{z}\right)$
Fresnel integral; 7.2.7
$C_{1}(\NVar{z})=\mathop{C\/}\nolimits\!\left(\sqrt{2/\pi}z\right)$
alternative notation for the Fresnel integral; §7.1
$C_{2}(\NVar{z})=\mathop{C\/}\nolimits\!\left(\sqrt{2z/\pi}\right)$
alternative notation for the Fresnel integral; §7.1
$\mathop{c_{\NVar{k}}\/}\nolimits\!\left(\NVar{n}\right)$
Ramanujan’s sum; 27.10.4
$\mathop{C_{\NVar{\ell}}\/}\nolimits\!\left(\NVar{\eta}\right)$
normalizing constant for Coulomb radial functions; 33.2.5
$\mathop{c_{\NVar{m}}\/}\nolimits\!\left(\NVar{n}\right)$
number of compositions of $n$ into exactly $m$ parts; §26.11
$\mathop{C_{\NVar{n}}\/}\nolimits\!\left(\NVar{x}\right)$
dilated Chebyshev polynomial; 18.1.3
$\mathop{\mathscr{C}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z}\right)$
cylinder function; §10.2(ii)
$\mathop{C^{\NVar{n}}\/}\nolimits(\NVar{I})$ or $\mathop{C^{\NVar{n}}\/}\nolimits(\NVar{a,b})$
continuously differentiable $n$ times on an interval $I$ or $(a,b)$; §1.4(iii)
$\mathop{C^{\infty}\/}\nolimits(\NVar{I})$ or $\mathop{C^{\infty}\/}\nolimits(\NVar{a,b})$
infinitely differentiable on an interval $I$ or $(a,b)$; §1.4(iii)
$\mathop{C^{(\NVar{\lambda})}_{\NVar{\alpha}}\/}\nolimits\!\left(\NVar{z}\right)$
Gegenbauer function; §15.9(iii)
$\mathop{C^{(\NVar{\lambda})}_{\NVar{n}}\/}\nolimits\!\left(\NVar{x}\right)$
ultraspherical (or Gegenbauer) polynomial; Table 18.3.1
$\mathop{c\/}\nolimits\!\left(\NVar{\mathrm{condition}},\NVar{n}\right)$
restricted number of compositions of $n$; §26.11
$\mathop{C_{\NVar{n}}\/}\nolimits\!\left(\NVar{x};\NVar{a}\right)$
Charlier polynomial; Table 18.19.1
$C_{\NVar{n}}^{\NVar{m}}(\NVar{z},\NVar{\xi})$
Ince polynomials; §28.31(ii)
$\mathop{c\/}\nolimits\!\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)$
irregular Coulomb function; 33.14.9
$C(\NVar{f},\NVar{h})(\NVar{x})$
cardinal function; 3.3.43
$\mathop{C_{\NVar{n}}\/}\nolimits\!\left(\NVar{x};\NVar{\beta}\,|\,\NVar{q}\right)$
continuous $q$-ultraspherical polynomial; 18.28.13
$\mathop{\mathrm{cd}\/}\nolimits\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; 22.2.8
$\mathop{\mathit{cdE}^{\NVar{m}}_{2\NVar{n}+2}\/}\nolimits\!\left(\NVar{z},% \NVar{k^{2}}\right)$
Lamé polynomial; 29.12.7
$\mathop{\mathrm{ce}_{\NVar{n}}\/}\nolimits\!\left(\NVar{z},\NVar{q}\right)$
Mathieu function; §28.2(vi)
$\mathop{\mathrm{Ce}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z},\NVar{q}\right)$
modified Mathieu function; 28.20.3
$\mathop{\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\/}\nolimits\!\left(\NVar{z},\NVar% {k^{2}}\right)$
Lamé polynomial; 29.12.3
$\mathop{\mathrm{ce}_{\NVar{\nu}}\/}\nolimits\!\left(\NVar{z},\NVar{q}\right)$
Mathieu function of noninteger order; 28.12.12
$\mathrm{ceh}_{\NVar{n}}(\NVar{z},\NVar{q})=\mathop{\mathrm{Ce}_{n}\/}\nolimits% \!\left(z,q\right)$
notation used by Campbell (1955); §28.1
$\mathop{\mathrm{cel}\/}\nolimits\!\left(\NVar{k_{c}},\NVar{p},\NVar{a},\NVar{b% }\right)$
Bulirsch’s complete elliptic integral; 19.2.11
$\mathop{\chi\/}\nolimits\!\left(\NVar{n}\right)$
Dirichlet character; §27.8
$\chi(\NVar{n})$
ratio of gamma functions; §9.7(i)
$\mathop{\mathrm{Chi}\/}\nolimits\!\left(\NVar{z}\right)$
hyperbolic cosine integral; 6.2.16
$\mathop{\mathrm{Ci}\/}\nolimits\!\left(\NVar{z}\right)$
cosine integral; 6.2.11
$\mathop{\mathrm{Ci}\/}\nolimits\!\left(\NVar{a},\NVar{z}\right)$
generalized cosine integral; 8.21.2
$\mathop{\mathrm{ci}\/}\nolimits\!\left(\NVar{a},\NVar{z}\right)$
generalized cosine integral; 8.21.1
$\mathop{\mathrm{Cin}\/}\nolimits\!\left(\NVar{z}\right)$
cosine integral; 6.2.12
$\mathop{\mathrm{cn}\/}\nolimits\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; 22.2.5
$\mathrm{cn}(\NVar{z}\mathpunct{|}\NVar{m})=\mathop{\mathrm{cn}\/}\nolimits% \left(z,\sqrt{m}\right)$
alternative notation; §22.1
$\mathop{\cos\/}\nolimits\NVar{z}$
cosine function; 4.14.2
$\mathop{\mathrm{Cos}_{\NVar{q}}\/}\nolimits\!\left(\NVar{x}\right)$
$q$-cosine function; 17.3.6
$\mathop{\mathrm{cos}_{\NVar{q}}\/}\nolimits\!\left(\NVar{x}\right)$
$q$-cosine function; 17.3.5
$\mathop{\cosh\/}\nolimits\NVar{z}$
hyperbolic cosine function; 4.28.2
$\mathop{\cot\/}\nolimits\NVar{z}$
cotangent function; 4.14.7
$\mathop{\coth\/}\nolimits\NVar{z}$
hyperbolic cotangent function; 4.28.7
$\mathop{\mathrm{cs}\/}\nolimits\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; 22.2.9
$\mathop{\csc\/}\nolimits\NVar{z}$
cosecant function; 4.14.5
$\mathop{\mathrm{csch}\/}\nolimits\NVar{z}$
hyperbolic cosecant function; 4.28.5
$\mathop{\mathrm{curl}}$
of vector-valued function; 1.6.22