# Index F

ABCDE♦F♦GHIJKLMNOPQRSTUVWZ
• Faà di Bruno’s formula
• for derivatives
• Fabry’s transformation
• differential equations
• factorials (rising or falling)
• factorization
• of integers
• via Weierstrass elliptic functions
• fast Fourier transform
• Fay’s trisecant identity
• Riemann theta functions with characteristics
• generalizations
• Fejér kernel
• Fourier integral
• Fourier series
• Fermat numbers
• number theory
• Fermat’s last theorem
• Bernoulli and Euler numbers and polynomials
• Fermi–Dirac integrals
• approximations
• computation
• definition
• relation to polylogarithms
• tables
• uniform asymptotic approximation
• Ferrers board
• Ferrers function
• of the first kind
• integral equation for Lamé functions
• Ferrers functions
• analytic continuation
• applications
• spherical harmonics
• spheroidal harmonics
• asymptotic approximations
• behavior at singularities
• computation
• connection formulas
• cross-products
• definitions
• degree
• derivatives
• with respect to degree or order
• differential equation
• generating functions
• graphics
• integer degree and order
• integer order
• integral representations
• integrals
• definite
• indefinite
• Laplace transforms
• Mellin transforms
• orthogonality properties
• notation
• of the first kind
• of the second kind
• order
• orthogonality
• recurrence relations
• reflection formulas
• relations to other functions
• elliptic integrals
• hypergeometric function
• Legendre polynomials
• ultraspherical polynomials
• Rodrigues-type formulas
• special values
• sums
• tables
• trigonometric expansions
• uniform asymptotic approximations
• large degree
• large order
• Wronskians
• zeros
• Ferrers graph
• Feynman diagrams
• Appell functions
• Feynman path integrals
• theta functions
• Fibonacci numbers
• fine structure constant
• Coulomb functions
• finite Fourier series
• number theory
• fixed point
• floating-point arithmetic
• bits
• format width
• significant
• double precision
• exponent
• fractional part
• IEEE standard
• machine epsilon
• machine number
• machine precision
• overflow
• rounding
• by chopping
• down
• symmetric
• to nearest machine number
• significand
• single precision
• underflow
• Floquet solutions
• Hill’s equation
• Mathieu’s equation
• Floquet’s theorem
• Hill’s equation
• Mathieu’s equation
• fluid dynamics
• elliptic integrals
• Legendre polynomials
• Riemann theta functions
• Struve functions
• fold canonical integral
• bifurcation set
• differential equation
• integral identity
• relation to Airy function
• zeros
• fold catastrophe
• Fourier–Bessel expansion
• Bessel functions
• computation
• Fourier cosine and sine transforms
• definition
• generalized
• inversion
• Parseval’s formula
• tables
• Fourier integral
• asymptotic expansions
• Dirac delta
• Fejér kernel
• Poisson kernel
• summability
• Fourier series
• Bessel’s inequality
• coefficients
• compendia
• convergence
• definition
• differentiation
• Dirac delta
• Fejér kernel
• finite
• number theory
• integration
• Parseval’s formula
• Poisson kernel
• Poisson’s summation formula
• properties
• summability
• uniqueness
• Fourier-series expansions
• nonuniformity of convergence
• piecewise continuous functions
• Fourier transform
• convergence
• convolution
• definitions
• discrete
• distributions
• fast
• group
• hypergeometric function
• inversion
• Parseval’s formula
• tables
• tempered distributions
• uniqueness
• fractals
• fractional derivatives
• fractional integrals
• asymptotic expansions
• definition
• fractional linear transformation
• Fresnel integrals
• applications
• Cornu’s spiral
• interference patterns
• physics and astronomy
• probability theory
• statistics
• approximations
• asymptotic expansions
• exponentially-improved
• auxiliary functions
• computation
• definition
• expansions in spherical Bessel functions
• graphics
• integrals
• Laplace transforms
• interrelations
• notation
• power-series expansions
• relations to other functions
• Anger–Weber functions
• auxiliary functions
• confluent hypergeometric functions
• error functions
• generalized hypergeometric functions
• symmetry
• tables
• values at infinity
• zeros
• asymptotic expansions
• tables
• Freud weight function
• Frobenius’ identity
• Riemann theta functions with characteristics
• Fuchsian equation
• classification of parameters
• definitions
• normal form
• polynomial solutions
• relation to Heun’s equation
• functions
• analytic
• analytically continued
• continuous
• continuously differentiable
• convex
• decreasing
• defined by contour integrals
• differentiable
• entire
• harmonic
• holomorphic
• increasing
• inverse
• limits
• many-valued
• meromorphic
• monotonic
• multivalued
• nondecreasing
• nonincreasing
• of a complex variable
• of bounded variation
• of compact support
• of matrix argument
• strictly decreasing
• strictly increasing
• strictly monotonic
• support of
• vector-valued
• functions of matrix argument
• Laplace transform
• orthogonal invariance
• fundamental theorem of arithmetic
• fundamental theorem of calculus