# Index T

ABCDEFGHIJKLMNOPQRS♦T♦UVWZ
• tangent function
• tangent numbers
• tables
• Taylor series
• asymptotic approximations for coefficients
• Taylor’s theorem
• one variable
• two variables
• tempered distributions
• convergence
• Fourier transform
• term-by-term integration
• terminant function
• incomplete gamma functions
• tesseral harmonics
• test functions
• distributions
• Theorem of Ince
• Mathieu’s equation
• theta functions
• applications
• mathematical
• physical
• combined
• computation
• derivatives
• of ratios
• discrete analog
• double products
• duplication formula
• Fourier series
• fundamental parallelogram
• generalizations
• graphics
• complex variables
• real variables
• infinite products
• integrals
• Jacobi’s identity
• Jacobi’s inversion formula
• Jacobi’s original notation
• Jacobi’s triple product
• Landen transformation
• Laplace transform with respect to lattice parameter
• lattice parameter
• transformation of
• lattice points
• limit forms as $\Im\tau\rightarrow 0+$
• McKean and Moll’s
• Mellin transform with respect to lattice parameter
• modular transformations
• multidimensional, see Chapter 21.
• Neville’s
• nome
• rectangular case
• transformation of
• notation
• periodicity
• permutation symmetry
• power series
• quasi-periodicity
• Ramanujan’s
• Ramanujan’s change of base
• rectangular case
• relations to other functions
• Dedekind’s eta function
• elliptic integrals
• elliptic modular function
• Jacobi’s epsilon function
• Jacobian elliptic functions
• modular functions
• Riemann zeta function
• symmetric elliptic integrals
• Weierstrass elliptic functions
• Riemann
• Riemann with characteristics
• sums of squares
• tables
• translation by half-periods
• values at $z=0$
• Watson’s expansions
• Watson’s identities
• with characteristics
• zeros
• Thomae transformation
• ${{}_{3}F_{2}}$ functions of matrix argument
• $\mathit{3j},\mathit{6j},\mathit{9j}$ symbols
• relation to generalized hypergeometric functions
• $\mathit{3j}$ symbols
• angular momenta
• applications
• approximations for large parameters
• computation
• definition
• Gaunt coefficient
• Gaunt’s integral
• generating functions
• graphical method
• notation
• orthogonality
• projective quantum numbers
• recursion relations
• Regge symmetries
• relations to other functions
• Legendre functions
• rotation matrices
• spherical harmonics
• representation as
• finite sum of algebraic quantities
• generalized hypergeometric functions
• special cases
• summation convention
• sums
• symmetry
• tables
• triangle conditions
• zeros
• Toda equation
• Hermite polynomials
• tomography
• confluent hypergeometric functions
• tops
• Jacobian elliptic, or hyperelliptic, integrals
• toroidal coordinates
• toroidal functions
• applications
• definitions
• hypergeometric representations
• integral representations
• sums
• Whipple’s formula
• torus
• complex
• transcendental equations
• asymptotic solutions
• transcendental functions
• transition points
• transport equilibrium
• generalized exponential integral
• triangle conditions
• $\mathit{3j}$ symbols
• triangle inequality
• triangles
• solution of
• triangular matrices
• confluent hypergeometric functions
• triconfluent Heun equation
• trigonometric functions
• analytic properties
• applications
• cubic equations
• solution of triangles and spherical triangles
• approximations
• Chebyshev-series expansions
• computation
• conformal maps
• continued fractions
• definitions
• derivatives
• differential equations
• elementary properties
• graphics
• complex argument
• real argument
• identities
• inequalities
• infinite products
• integrals
• definite
• indefinite
• inverse
• Laurent series
• limits
• Maclaurin series
• moduli
• multiples of argument
• notation
• orthogonality
• partial fractions
• periodicity
• poles
• real and imaginary parts
• relations to hyperbolic functions
• special values
• squares and products
• sums
• tables
• zeros
• triple integrals
• truncated exponential series
• turning points
• fractional or multiple
• two-body relativistic scattering
• Lamé polynomials