# Index D

ABC♦D♦EFGHIJKLMNOPQRSTUVWZ
• Darboux’s method
• asymptotic approximations of sums and sequences
• Dawson’s integral
• applications
• approximations
• computation
• definition
• generalized
• graphics
• integral representation
• notation
• relation to error functions
• relation to parabolic cylinder functions
• tables
• de Branges–Wilson beta integral
• De Moivre’s theorem
• trigonometric functions
• Debye functions
• Dedekind modular function
• functional equation
• Dedekind sums
• number theory
• Dedekind’s eta function, see modular functions.
• Dedekind’s modular function, see modular functions.
• del operator
• Delannoy numbers
• definition
• generating functions
• recurrence relation
• relation to lattice paths
• table
• delta sequence
• delta wing equation
• Lamé polynomials
• derivatives
• chain rule
• definition
• distributional
• Faà di Bruno’s formula
• Jacobian
• L’Hôpital’s rule
• left-hand
• Leibniz’s formula
• mean value theorem
• notation
• of distribution
• partial
• right-hand
• Descartes’ rule of signs (for polynomials)
• determinants
• alternants
• Cauchy
• circulant
• cofactor
• definition
• Hankel
• inequalities
• infinite
• convergence
• Hill’s type
• Krattenthaler’s formula
• minor
• notation
• persymmetric
• properties
• Vandermonde
• diatomic molecules
• hypergeometric function
• difference equations
• asymptotic solutions
• distinguished solutions
• minimal solutions
• numerical solution
• backward recursion method
• boundary-value methods
• homogeneous equations
• inhomogeneous equations
• normalizing factor
• stability
• recessive solutions
• difference operators
• backward
• central in imaginary direction
• forward
• differentiable functions
• differential equations
• asymptotic solutions
• change of variables
• elimination of first derivative
• Liouville transformation
• point at infinity
• classification of singularities
• closed-form solutions
• dominant solutions
• Fuchs–Frobenius theory
• homogeneous
• indices differing by an integer
• indicial equation
• inhomogeneous
• solution by variation of parameters
• irregular singularity
• nonhomogeneous, see inhomogeneous.
• numerical solution
• boundary-value problems
• eigenfunctions
• eigenvalues
• initial-value problems
• Runge–Kutta method
• stability
• Sturm–Liouville eigenvalue problems
• Taylor-series methods
• numerically satisfactory solutions
• of arbitrary order
• ordinary point
• rank of singularity
• recessive solutions
• regular singularity
• Schwarzian derivative
• solutions
• existence
• fundamental pair
• in series of Chebyshev polynomials
• in series of classical orthogonal polynomials
• linearly independent
• products
• Wronskian
• subdominant solutions, see recessive solutions.
• with a parameter
• differentiation
• Cauchy–Riemann equations
• numerical
• analytic functions
• Lagrange’s formula for equally-spaced nodes
• partial derivatives
• of integrals
• partial
• diffraction catastrophes
• notation
• scaling laws
• diffraction of light
• Fresnel integrals and Cornu’s spiral
• diffraction problems
• Mathieu functions
• diffusion equations
• theta functions
• diffusion problems
• Mathieu functions
• digamma function, see psi function.
• dilogarithms
• analytic properties
• approximations
• computation
• definition
• graphics
• principal branch (or value)
• tables
• Dirac delta
• delta sequences
• integral representations
• Airy functions
• Bessel functions
• Coulomb functions
• Fourier
• spherical Bessel functions
• mathematical definitions
• series representations
• Fourier
• Hermite polynomials
• Laguerre polynomials
• Legendre polynomials
• spherical harmonics
• Dirac delta distribution
• Dirac delta function, see Dirac delta.
• Dirac equation
• Coulomb functions
• Dirichlet characters
• Gauss sum
• Dirichlet $L$-functions
• analytic properties
• definition
• functional equation
• infinite products
• tables
• zeros
• Dirichlet problem
• with toroidal symmetry
• Dirichlet product (or convolution)
• Dirichlet series
• generating function
• Dirichlet’s divisor problem
• number theory
• Dirichlet’s theorem
• prime numbers in arithmetic progression
• discontinuity
• discrete Fourier transform
• discrete $q$-Hermite I and II polynomials
• discriminant
• of a polynomial
• discriminant function
• number theory
• functional equation
• disk
• around infinity
• open
• disk polynomials
• dislocation theory
• Heun functions
• distribution function
• Painlevé transcendents
• distribution functions
• connection with
• incomplete beta functions
• incomplete gamma functions
• distributional derivative
• distributions
• convergence
• convolutions
• derivatives
• Dirac delta
• distributional derivative
• Fourier transforms
• Heaviside function
• linear functionals
• of derivatives
• regular
• regularization
• several variables
• singular
• support
• tempered
• test function space
• test functions
• convergence
• divergence theorem
• divergent integrals
• regularization
• divided differences
• definition
• integral representation
• divisor function
• number theory
• Dixon’s $\mathop{{{}_{3}F_{2}}\/}\nolimits(1)$ sum
• $q$-analog
• Dixon’s sum
• F. H. Jackson’s $q$-analog
• domain
• closed
• cut
• simply-connected
• dominated convergence theorem
• infinite series
• double gamma function
• double integrals
• change of order of integration
• change of variables
• infinite
• double sequence
• convergence
• double series
• convergence
• doubly-confluent Heun equation
• Dougall’s $\mathop{{{}_{7}F_{6}}\/}\nolimits(1)$ sum
• F. H. Jackson’s $q$-analog
• Dougall’s bilateral sum
• Dougall’s expansion
• associated Legendre functions
• dual Hahn polynomials
• Duffing’s equation
• Jacobian elliptic functions
• dynamical systems
• Mathieu functions
• Painlevé transcendents
• Dyson’s integral
• gamma function