# Index C

• calculus
• complex variable
• one variable
• two or more variables
• calculus of finite differences
• canonical integrals
• applications
• acoustics
• caustics
• integrals with coalescing critical points
• optics
• quantum mechanics
• asymptotic approximations
• computation
• convergent series
• definitions
• differential equations
• integral identities
• notation
• relations to other functions
• Airy function
• Pearcey integral
• special cases
• symmetries
• visualizations of modulus
• visualizations of phase
• zeros
• cardinal function
• cardinal monosplines
• cardinal spline functions
• Carmichael numbers
• number theory
• Casimir forces
• Bernoulli polynomials
• Casimir operator
• Casimir–Polder effect
• Riemann zeta function
• Catalan numbers
• definitions
• generating function
• identities
• limiting forms
• recurrence relations
• relation to lattice paths
• table
• Catalan’s constant
• Riemann zeta function
• Cauchy determinant
• Cauchy principal values
• integrals
• Cauchy–Riemann equations
• Cauchy–Schwarz inequalities for sums and integrals
• Cauchy’s integral formula
• for derivatives
• Cauchy’s theorem
• caustics
• Airy functions
• canonical integrals
• Cayley’s identity for Schwarzian derivatives
• central differences in imaginary direction
• Cesàro means
• Cesàro summability
• chain rule
• for derivatives
• characteristic equation
• difference equations
• differential equations
• characteristics
• Riemann theta functions
• characters
• number theory
• Dirichlet
• induced modulus
• orthogonality relation
• primitive
• principal
• real
• Charlier polynomials
• Chebyshev polynomials
• applications
• approximation theory
• numerical solutions of differential equations
• computation
• continued fractions
• definition
• derivatives
• differential equations
• dilated
• expansions in series of
• explicit representations
• generating functions
• graphs
• inequalities
• integral representations
• integrals
• interrelations with other classical orthogonal polynomials
• linearization formula
• local maxima and minima
• monic
• notation
• of the first, second, third, and fourth kinds
• orthogonality properties
• with respect to integration
• with respect to summation
• recurrence relations
• relations to other functions
• hypergeometric function
• Jacobi polynomials
• trigonometric functions
• Rodrigues formula
• shifted
• special values
• standardization
• symmetry
• tables
• of coefficients
• upper bounds
• weight functions
• zeros
• Chebyshev $\psi$-function
• Chebyshev-series expansions
• complex variables
• computation of coefficients
• relation to minimax polynomials
• summation
• chemical reactions
• $\mathit{3j},\mathit{6j},\mathit{9j}$ symbols
• chi-square distribution function
• incomplete gamma functions
• Chinese remainder theorem
• number theory
• Christoffel coefficients (or numbers)
• Christoffel–Darboux formula
• confluent form
• Chu–Vandermonde identity
• hypergeometric function
• circular trigonometric functions
• classical dynamics
• Jacobian elliptic functions
• Weierstrass elliptic functions
• classical orthogonal polynomials
• applications
• approximation theory
• Bieberbach conjecture
• integrable systems
• random matrix theory
• Riemann–Hilbert problems
• asymptotic approximations
• characterizations
• computation
• connection formulas
• contiguous relations
• continued fractions
• definitions
• derivatives
• differential equations
• discriminant
• expansions in series of
• explicit representations
• Fourier transforms
• generating functions
• in two or more variables
• inequalities
• local maxima and minima
• positive sums
• Turán-type
• upper bounds
• integral representations
• for products
• integrals
• compendia
• interrelations
• limiting forms
• linear
• with other orthogonal polynomials
• Laplace transforms
• limiting forms
• Mehler–Heine type formulas
• linearization formulas
• local maxima and minima
• Mellin transforms
• multiplication theorems
• notations
• orthogonality properties
• parameter constraints
• Poisson kernels
• recurrence relations
• relations to other functions
• confluent hypergeometric functions
• generalized hypergeometric functions
• hypergeometric function
• standardization
• sums
• Bateman-type
• compendia
• tables
• of coefficients
• upper bounds
• weight functions
• zeros
• asymptotic approximations
• distribution
• inequalities
• classical theta functions, see theta functions.
• Clausen’s integral
• tables
• Clebsch–Gordan coefficients
• relation to generalized hypergeometric functions
• Clenshaw’s algorithm
• Chebyshev series
• classical orthogonal polynomials
• closed point set
• closure
• of interval
• of point sets in complex plane
• coaxial circles
• symmetric elliptic integrals
• coding theory
• combinatorics
• Krawtchouk and $q$-Racah polynomials
• cofactor, see determinants.
• coherent states
• generalized
• confluent hypergeometric functions
• combinatorial design
• combinatorics
• applications
• mathematical
• physical
• generalized hypergeometric functions
• hypergeometric identities
• Painlevé transcendents
• compact set
• complementary error function, see error functions.
• complementary exponential integral
• completely multiplicative functions
• completeness relation
• eigenfunctions
• continuous spectrum
• completness relation
• eigenfunctions
• discrete spectrum
• complex numbers
• arithmetic operations
• complex conjugates
• DeMoivre’s theorem
• imaginary part
• modulus
• phase
• polar representation
• powers
• real part
• triangle inequality
• complex physical systems
• incomplete gamma functions
• complex tori
• theta functions
• computer arithmetic
• generalized exponentials and logarithms
• computer-aided design
• Cornu’s spiral
• conductor
• generalized Bernoulli polynomials
• confluent Heun equation
• applications
• properties of solutions
• special cases
• of matrix argument
• asymptotic approximations
• computation
• definition
• first kind
• Laguerre form
• notation
• properties
• relations to Bessel functions of matrix argument
• second kind
• relations to other functions
• Airy functions
• Bessel and Hankel functions
• classical orthogonal polynomials
• Coulomb functions
• error functions
• exponential integrals
• generalized Bessel polynomials
• generalized exponential integral
• Hahn class orthogonal polynomials
• modified Bessel functions
• parabolic cylinder functions
• repeated integrals of error functions
• sine and cosine integrals
• conformal mapping
• generalized hypergeometric functions
• hypergeometric function
• Jacobian elliptic functions
• modular functions
• symmetric elliptic integrals
• Weierstrass elliptic functions
• congruence of rational numbers
• conical functions
• applications
• asymptotic approximations
• large degree
• large order
• behavior at singularities
• connection formulas
• definitions
• degree
• differential equation
• generalized Mehler–Fock transformation
• graphics
• integral representation
• integrals with respect to degree
• notation
• order
• tables
• trigonometric expansion
• Wronskians
• zeros
• connected point set
• constants
• roots of
• contiguous relations
• continued fractions
• applications
• approximants
• canonical denominator (or numerator)
• contraction
• convergence
• convergents
• existence of
• determinant formula
• equivalent
• even part
• extension
• fractional transformations
• $J$-fraction
• Jacobi fraction
• associated
• notation
• numerical evaluation
• backward recurrence
• forward recurrence
• forward series recurrence
• odd part
• Pringsheim’s theorem
• quotient-difference algorithm
• recurrence relations
• relation to power series
• $S$-fraction
• series
• Stieltjes fraction
• Van Vleck’s theorem
• continuous dual Hahn polynomials
• continuous dynamical systems and mappings
• Painlevé transcendents
• continuous function
• at a point
• notation
• of two variables
• on a point set
• on a region
• on an interval
• on the left (or right)
• piecewise
• removable discontinuity
• sectionally
• simple discontinuity
• continuous Hahn polynomials
• continuous $q$-Hermite polynomials
• asymptotic approximations to zeros
• continuous $q$-ultraspherical polynomials
• continuous spectra
• eigenfunction expansions
• second order differential operators
• contour
• simple
• simple closed
• convergence
• acceleration
• cubic
• geometric
• linear
• local
• of the $p$th order
• convex functions
• coordinate systems
• cylindrical
• ellipsoidal
• elliptic
• elliptical
• oblate spheroidal
• parabolic cylinder
• paraboloid of revolution
• paraboloidal
• polar
• projective
• prolate spheroidal
• spherical (or spherical polar)
• sphero-conal
• toroidal
• corecursive orthogonal polynomials
• Cornu’s spiral
• applications
• connection with Fresnel integrals
• cosecant function
• cosine function
• cosine integrals
• analytic continuation
• applications
• approximations
• asymptotic expansions
• exponentially-improved
• auxiliary functions
• Chebyshev-series expansions
• computation
• definition
• expansion in spherical Bessel functions
• generalized
• graphics
• hyperbolic analog
• analytic continuation
• integral representations
• integrals
• Laplace transform
• notation
• power series
• principal value
• relations to exponential integrals
• sums
• tables
• value at infinity
• zeros
• asymptotic expansion
• computation
• cosine transform
• eigenfunction expansion
• Cosines
• Dirac delta
• cosmology
• confluent hypergeometric functions
• incomplete beta functions
• cotangent function
• Coulomb excitation of nuclei
• Coulomb field
• Coulomb functions
• Dirac delta
• Coulomb functions: variables $r,\epsilon$
• analytic properties
• applications
• asymptotic approximations and expansions for large $\left|r\right|$
• asymptotic expansions as $\epsilon\rightarrow 0$
• uniform
• case $\epsilon=0$
• complex variables and parameters
• computation
• conversions between variables and parameters
• definitions
• derivatives
• expansions in Airy functions
• expansions in Bessel functions
• expansions in modified Bessel functions
• functions $f(\epsilon,\ell;r),h(\epsilon,\ell;r)$
• functions $s(\epsilon,\ell;r),c(\epsilon,\ell;r)$
• graphics
• integral representations for Dirac delta
• limiting forms for large $\ell$
• power-series expansions in $r$
• power-series expansions in $\epsilon$
• recurrence relations
• relations to other functions
• confluent hypergeometric functions
• Coulomb functions with variables $\rho,\eta$
• Whittaker functions
• scaling of variables and parameters
• tables
• Wronskians
• Coulomb functions: variables $\rho,\eta$
• analytic properties
• applications
• asymptotic expansions
• large $\eta$
• large $\rho$
• uniform expansions
• case $\eta=0$
• complex variable and parameters
• computation
• continued fractions
• conversions between variables and parameters
• cross-product
• definitions
• derivatives
• expansions in Airy functions
• expansions in Bessel functions
• expansions in modified Bessel functions
• expansions in spherical Bessel functions
• functions $F_{\ell}(\eta,\rho),G_{\ell}(\eta,\rho),{H^{\pm}_{\ell}}(\eta,\rho)$
• graphics
• integral representations
• limiting forms
• large $\ell$
• large $\left|\eta\right|$
• large $\rho$
• small $\left|\eta\right|$
• small $\rho$
• normalizing constant
• phase shift (or phase)
• power-series expansions in $\rho$
• recurrence relations
• relations to other functions
• confluent hypergeometric functions
• Coulomb functions with variables $r,\epsilon$
• Whittaker functions
• scaling of variables and parameters
• tables
• transition region
• WKBJ approximations
• Wronskians
• Coulomb phase shift
• Coulomb potential barriers
• Coulomb potentials
• $q$-hypergeometric function
• Coulomb Problem in 3D
• Coulomb spheroidal functions
• as confluent Heun functions
• Coulomb wave equation
• irregular solutions
• regular solutions
• singularities
• turning points
• Coulomb wave functions
• Coulomb–Pollaczek polynomials
• and Coulomb Schrödinger equation
• and Coulomb wave functions
• attractive
• continuous weight function on $[-1,1]$
• discrete weights
• repulsive
• counting techniques
• critical phenomena
• elliptic integrals
• hypergeometric function
• critical points
• coalescing
• cross ratio
• cryptography
• Weierstrass elliptic functions
• cubature
• for disks and squares
• cubic equation
• resolvent
• cubic equations
• solutions as trigonometric and hyperbolic functions
• curve
• piecewise differentiable
• simple closed
• cusp bifurcation set
• formula
• picture
• cusp canonical integral
• zeros
• table
• cusp catastophe
• cuspoids
• normal forms
• cut
• domain
• neighborhood
• cycle
• Riemann surface
• cyclic identities
• Jacobian elliptic functions
• cyclotomic fields
• Bernoulli and Euler polynomials
• cylinder functions