# Index L

ABCDEFGHIJK♦L♦MNOPQRSTUVWZ
• L’Hôpital’s rule for derivatives
• Lagrange interpolation
• abscissas
• coefficients
• equally-spaced nodes
• error term
• formula
• Newton’s interpolation formula
• nodal polynomials
• nodes
• polynomial
• remainder terms
• via divided differences
• Lagrange inversion theorem
• extended
• Lagrange’s formula for reversion of series
• Laguerre functions
• associated
• Laguerre polynomials §18.3, see also classical orthogonal polynomials.
• addition theorem
• applications
• Schrödinger equation
• asymptotic approximations
• computation
• continued fraction
• derivatives
• differential equations
• Dirac delta
• expansions in series of
• explicit representations
• Fourier transforms
• generalized
• generating functions
• graphics
• inequalities
• Turán-type
• integral representations
• integrals
• fractional
• indefinite
• interrelations with other orthogonal polynomials
• Laplace transform
• leading coefficients
• limiting form as a Bessel function
• limits to monomials
• local maxima and minima
• Mellin transform
• monic
• multiplication theorem
• normalization
• notation
• orthogonality properties
• parameter constraint
• Poisson kernels
• recurrence relations
• relation to confluent hypergeometric functions
• Rodrigues formula
• tables
• of coefficients
• of zeros
• tables of zeros
• upper bounds
• value at $z=0$
• weight function
• zeros
• asymptotic behavior
• tables
• Lambert series
• number theory
• Lambert $\mathop{W\/}\nolimits$-function
• applications
• asymptotic expansions
• computation
• definition
• graphs
• integral representations
• notation
• principal branch
• other branches
• properties
• Lamé functions
• algebraic
• applications
• conformal mapping
• physical
• rotation group
• sphero-conal coordinates
• asymptotic expansions
• computation
• definition
• differential equation, see Lamé’s equation.
• eigenvalues
• asymptotic expansions
• coalescence
• computation
• continued-fraction equation
• definition
• distribution
• graphics
• interlacing
• limiting forms
• notation
• parity
• periods
• power-series expansions
• special cases
• tables
• Fourier series
• graphics
• integral equations
• limiting forms
• normalization
• notation
• order
• orthogonality
• parity
• period
• relations to Heun functions
• relations to Lamé polynomials
• special cases
• with imaginary periods
• with real periods
• zeros
• Lamé polynomials
• algebraic form
• applications
• ellipsoidal harmonics
• physical
• spherical harmonics
• asymptotic expansions
• Chebyshev series
• coefficients
• computation
• definition
• eigenvalues
• asymptotic expansions
• computation
• graphics
• elliptic-function form
• explicit formulas
• Fourier series
• graphics
• notation
• orthogonality
• periodicity
• relation to Lamé functions
• tables
• zeros
• computation
• electrostatic interpretation
• Lamé wave equation
• Lamé–Wangerin functions
• Lamé’s equation
• algebraic form
• eigenfunctions
• eigenvalues
• Jacobian elliptic-function form
• other forms
• relation to Heun’s equation
• second solution
• singularities
• stability
• trigonometric form
• Weierstrass elliptic-function form
• Lanczos tridiagonalization of a symmetric matrix
• Lanczos vectors
• Landen transformations
• Jacobian elliptic functions
• theta functions
• Laplace equation
• $\mathit{3j},\mathit{6j},\mathit{9j}$ symbols
• Laplace transform
• analyticity
• asymptotic expansions for large parameters
• asymptotic expansions for small parameters
• convergence
• convolution
• definition
• derivatives
• differentiation
• for functions of matrix argument
• analytic properties
• convolution theorem
• definition
• inversion formula
• integration
• inversion
• notation
• numerical inversion
• of periodic functions
• tables
• translation
• uniqueness
• Laplace’s equation
• Bessel functions
• for elliptical cones
• spherical coordinates
• symmetric elliptic integrals
• toroidal coordinates
• Laplace’s method for asymptotic expansions of integrals
• Laplacian
• cylindrical coordinates
• ellipsoidal coordinates
• numerical approximations
• oblate spheroidal coordinates
• parabolic cylinder coordinates
• polar coordinates
• prolate spheroidal coordinates
• spherical coordinates
• lattice
• for elliptic functions
• lattice models of critical phenomena
• elliptic integrals
• lattice parameter
• theta functions
• lattice paths
• definition
• $k$-dimensional
• lattice walks
• Appell functions
• generalized hypergeometric functions
• Laurent series
• asymptotic approximations for coefficients
• Lauricella’s function
• relation to symmetric elliptic integrals
• Lax pairs
• classical orthogonal polynomials
• Painlevé transcendents
• layered materials
• elliptic integrals
• least squares approximations
• conditioning
• normal equations
• orthogonal functions with respect to weighted summation
• Lebesgue constants
• asymptotic behavior
• Legendre functions §14.1, see also associated Legendre functions and Ferrers functions.
• complex degree
• Legendre functions on the cut, see Ferrers functions.
• Legendre polynomials §18.3, see also classical orthogonal polynomials.
• addition theorem
• applications
• Schrödinger equation
• associated
• asymptotic approximations
• computation
• continued fraction
• definition
• differential equation
• Dirac delta
• expansions in series of
• explicit representations
• Fourier transforms
• generating functions
• graphs
• inequalities
• Turán-type
• integral representations
• for products
• integrals
• Nicholson-type
• interrelations with other orthogonal polynomials
• large degree
• leading coefficients
• Mellin transforms
• monic
• normalization
• notation
• orthogonality properties
• recurrence relations
• relations to other functions
• associated Legendre functions
• Ferrers functions
• hypergeometric function
• $\mathit{3j}$ symbols
• Rodrigues formula
• shifted
• special values
• symmetry
• tables
• of coefficients
• of zeros
• tables of zeros
• weight function
• zeros
• tables
• Legendre symbol
• prime numbers
• Legendre’s elliptic integrals
• addition theorem
• applications
• mathematical
• physical
• approximations (except asymptotic)
• arithmetic-geometric mean
• asymptotic approximations
• change of amplitude
• change of modulus
• change of parameter
• circular cases
• complete
• computation
• connection formulas
• derivatives
• differential equations
• duplication formulas
• first, second, and third kinds
• Gauss transformation
• graphics
• hyperbolic cases
• imaginary-argument transformations
• imaginary-modulus transformations
• incomplete
• inequalities
• complete integrals
• incomplete integrals
• integration
• with respect to amplitude
• with respect to modulus
• Landen transformations
• ascending
• descending
• Laplace transforms
• limiting values
• notation
• power-series expansions
• quadratic transformations
• reciprocal-modulus transformation
• reduction of general elliptic integrals
• relations to other functions
• $\mathop{\mathrm{am}\/}\nolimits$ function
• Appell functions
• inverse Gudermannian function
• inverse Jacobian elliptic functions
• Jacobi’s epsilon function
• Jacobi’s zeta function
• Jacobian elliptic functions
• symmetric elliptic integrals
• theta functions
• Weierstrass elliptic functions
• special cases
• tables
• Legendre’s equation
• standard solutions
• Legendre’s relation
• Legendre’s elliptic integrals
• Legendre’s relation for the hypergeometric function
• generalized
• Leibniz’s formula for derivatives
• lemniscate arc length
• lemniscate constants
• lengths of plane curves
• Bernoulli’s lemniscate
• ellipse
• hyperbola
• Lerch’s transcendent
• definition
• properties
• relation to Hurwitz zeta function
• relation to polylogarithms
• level-index arithmetic
• Levi-Civita symbol for vectors
• Levin’s transformations
• application to asymptotic expansions
• for sequences
• Lie algebras
• $q$-series
• light absorption
• Voigt functions
• limit points (or limiting points)
• limits of functions
• of a complex variable
• of one variable
• of two complex variables
• of two variables
• line broadening function
• linear algebra , see also Gaussian elimination.
• condition numbers
• conditioning of linear systems
• error bounds
• a posteriori
• norms
• Euclidean
• of arbitrary order
• of matrices
• of vectors
• linear functional
• linear transformation
• Liouville transformation for differential equations
• Liouville–Green (or WKBJ) approximation
• for difference equations
• Liouville’s function
• number theory
• Liouville’s theorem for entire functions
• little $q$-Jacobi polynomials
• local maxima and minima
• locally analytic
• locally integrable
• logarithm function
• analytic properties
• approximations
• branch cut
• Briggs
• Chebyshev-series expansions
• common
• computation
• conformal maps
• continued fractions
• definition
• derivatives
• differential equations
• general base
• general value
• generalized
• graphics
• complex argument
• real argument
• hyperbolic
• identities
• inequalities
• integrals
• limits
• Napierian
• natural
• notation
• power series
• principal value
• real and imaginary parts
• special values
• sums
• tables
• values on the cut
• zeros
• logarithmic integral
• asymptotic expansion
• definition
• graph
• notation
• number-theoretic significance
• relation to exponential integrals
• Lommel functions
• asymptotic expansions for large argument
• computation
• definitions
• differential equation
• integral representations
• integrals
• notation
• power series
• reflection formulas
• relation to Anger–Weber functions
• series expansions
• Bessel functions
• power series
• Lucas numbers