DLMF: Notations C

Notations C

♦*♦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♦

$\subset$: is contained in; Common Notations and Definitions
$\subseteq$: is, or is contained in; Common Notations and Definitions
$\Complex$: complex plane (excluding infinity); Common Notations and Definitions
$\mathop{C\/}\nolimits\!\left(n\right)$: Catalan number; (26.5.1)
$\mathop{C\/}\nolimits(I)$ or $\mathop{C\/}\nolimits(a,b)$: continuous on an interval $I$ or $(a,b)$ ; §1.4(ii)
$\mathop{C^{{n}}\/}\nolimits(I)$ or $\mathop{C^{{n}}\/}\nolimits(a,b)$: continuously differentiable $n$ times on an interval $I$ or $(a,b)$ ; ¶ ‣ §1.4(iii)
$\mathop{C^{{\infty}}\/}\nolimits(I)$ or $\mathop{C^{{\infty}}\/}\nolimits(a,b)$: infinitely differentiable on an interval $I$ or $(a,b)$ ; ¶ ‣ §1.4(iii)
$\mathop{\chi\/}\nolimits\!\left(n\right)$: Dirichlet character; §27.8
$\mathop{C\/}\nolimits\!\left(z\right)$: Fresnel integral; (7.2.7)
$\chi(n)$: ratio of gamma functions; §9.7(i)
$\mathop{c\/}\nolimits\!\left(n\right)$: number of compositions of $n$ ; §26.11
$C_{1}(z)=\mathop{C\/}\nolimits\!\left(\sqrt{2/\pi}z\right)$: alternative notation for the Fresnel integral; §7.1
(with $\mathop{C\/}\nolimits\!\left(z\right)$ : Fresnel integral)
$C_{2}(z)=\mathop{C\/}\nolimits\!\left(\sqrt{2z/\pi}\right)$: alternative notation for the Fresnel integral; §7.1
(with $\mathop{C\/}\nolimits\!\left(z\right)$ : Fresnel integral)
$\mathop{\mathscr{C}_{{\nu}}\/}\nolimits\!\left(z\right)$: cylinder function; ¶ ‣ §10.2(ii)
$\mathop{C_{{n}}\/}\nolimits\!\left(x\right)$: dilated Chebyshev polynomial; (18.1.3)
$\mathop{C_{{\ell}}\/}\nolimits\!\left(\eta\right)$: normalizing constant for Coulomb radial functions; (33.2.5)
$\mathop{c_{{m}}\/}\nolimits\!\left(n\right)$: number of compositions of $n$ into exactly $m$ parts; §26.11
$\mathop{c_{{k}}\/}\nolimits\!\left(n\right)$: Ramanujan’s sum; (27.10.4)
$\mathop{C^{{(\lambda)}}_{{\alpha}}\/}\nolimits\!\left(z\right)$: Gegenbauer function; §15.9(iii)
$\mathop{C^{{(\lambda)}}_{{n}}\/}\nolimits\!\left(x\right)$: ultraspherical (or Gegenbauer) polynomial; Table 18.3.1
$\mathop{c\/}\nolimits\!\left(\mathrm{condition},n\right)$: restricted number of compositions of $n$ ; §26.11
$\mathop{C_{{n}}\/}\nolimits\!\left(x,a\right)$: Charlier polynomial; Table 18.19.1
$C_{n}^{m}(z,\xi)$: Ince polynomials; §28.31(ii)
$\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$: irregular Coulomb function; (33.14.9)
$C(f,h)(x)$: cardinal function; (3.3.43)
$\mathop{C_{{n}}\/}\nolimits\!\left(x;\beta\,|\, q\right)$: continuous $q$ -ultraspherical polynomial; (18.28.13)

$\mathop{\mathrm{cd}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.8)
$\mathop{\mathit{cdE}^{{m}}_{{2n+2}}\/}\nolimits\!\left(z,k^{2}\right)$: Lamé polynomial; (29.12.7)
$\mathop{\mathrm{Ce}_{{\nu}}\/}\nolimits\!\left(z,q\right)$: modified Mathieu function; (28.20.3)
$\mathop{\mathrm{ce}_{{n}}\/}\nolimits\!\left(z,q\right)$: Mathieu function; §28.2(vi)
$\mathop{\mathrm{ce}_{{\nu}}\/}\nolimits\!\left(z,q\right)$: Mathieu function of noninteger order; (28.12.12)
$\mathop{\mathit{cE}^{{m}}_{{2n+1}}\/}\nolimits\!\left(z,k^{2}\right)$: Lamé polynomial; (29.12.3)
$\mathrm{ceh}_{n}(z,q)=\mathop{\mathrm{Ce}_{{n}}\/}\nolimits\!\left(z,q\right)$: notation used by Campbell (1955); ¶ ‣ §28.1
(with $\mathop{\mathrm{Ce}_{{\nu}}\/}\nolimits\!\left(z,q\right)$ : modified Mathieu function)
$\mathop{\mathrm{cel}\/}\nolimits\!\left(k_{c},p,a,b\right)$: Bulirsch’s complete elliptic integral; (19.2.11)
$\mathop{\mathrm{Chi}\/}\nolimits\!\left(z\right)$: hyperbolic cosine integral; (6.2.16)
$\mathop{\mathrm{Ci}\/}\nolimits\!\left(z\right)$: cosine integral; (6.2.11)
$\mathop{\mathrm{Ci}\/}\nolimits\!\left(a,z\right)$: generalized cosine integral; (8.21.2)
$\mathop{\mathrm{ci}\/}\nolimits\!\left(a,z\right)$: generalized cosine integral; (8.21.1)
$\mathop{\mathrm{Cin}\/}\nolimits\!\left(z\right)$: cosine integral; (6.2.12)
$\mathrm{cn}(z\mathpunct{|}m)=\mathop{\mathrm{cn}\/}\nolimits\left(z,\sqrt{m}\right)$: alternative notation; §22.1
(with $\mathop{\mathrm{cn}\/}\nolimits\left(z,k\right)$ : Jacobian elliptic function)
$\mathop{\mathrm{cn}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.5)
$\mathop{\cos\/}\nolimits z$: cosine function; (4.14.2)
$\mathop{\mathrm{Cos}_{{q}}\/}\nolimits\!\left(x\right)$: $q$ -cosine function; (17.3.6)
$\mathop{\mathrm{cos}_{{q}}\/}\nolimits\!\left(x\right)$: $q$ -cosine function; (17.3.5)
$\mathop{\cosh\/}\nolimits z$: hyperbolic cosine function; (4.28.2)
$\mathop{\cot\/}\nolimits z$: cotangent function; (4.14.7)
$\mathop{\coth\/}\nolimits z$: hyperbolic cotangent function; (4.28.7)
$\mathop{\mathrm{cs}\/}\nolimits\left(z,k\right)$: Jacobian elliptic function; (22.2.9)
$\mathop{\csc\/}\nolimits z$: cosecant function; (4.14.5)
$\mathop{\mathrm{csch}\/}\nolimits z$: hyperbolic cosecant function; (4.28.5)
$\curl$: of vector-valued function; (1.6.22)