Index Index S Index U

Index T

• tangent function, see trigonometric functions.
• tangent numbers §24.15(ii)
  • tables Table 24.15.1
• Taylor series §1.10(i)
  • asymptotic approximations for coefficients §2.10(iv)
• Taylor’s theorem
  • one variable §1.10(i), §1.4(vi)
  • two variables §1.5(iii)
• tempered distributions §1.16(v), §1.16(vi), §2.6(ii)
  • convergence §1.16(v)
  • Fourier transform §1.16(vii)
• term-by-term integration §1.9(vii)
• terminant function §2.11(v)
  • incomplete gamma functions §8.22(i)
• tesseral harmonics §14.30(i)
• test functions
  • distributions §1.16(i)
• Theorem of Ince
  • Mathieu’s equation §28.2(iv), §28.5(i)
• theta functions §20.2(i)
  • addition formulas §20.7(ii)
  • applications
    • mathematical §20.12—§20.12(ii)
    • physical §20.13
  • combined §20.11(v)
  • computation §20.14
  • derivatives §20.4—§20.5(ii)
    • of ratios §20.7(vii)
  • discrete analog §20.11(i)
  • double products §20.5(iii)
  • duplication formula §20.7(iii)
  • Fourier series §20.2(i)
  • fundamental parallelogram §20.2(ii)
  • generalizations §20.11
  • graphics
    • complex variables §20.3(ii)—§20.3(iii)
    • real variables §20.3(i)—§20.3(i)
  • infinite products §20.5—§20.5(iii)
  • integrals §20.10
  • Jacobi’s identity §20.4(i)
  • Jacobi’s inversion formula §20.11(iii), §20.9(ii)
  • Jacobi’s original notation §20.1
  • Jacobi’s triple product §20.5(i)
  • Landen transformation §20.7(vi)
  • Laplace transform with respect to lattice parameter §20.10(ii)
  • lattice parameter §20.1
    • transformation of §20.7(viii)
  • lattice points §20.2(ii)
  • limit forms as $\mathrm{\Im }\tau \to 0+$ §20.13
  • McKean and Moll’s §20.1
  • Mellin transform with respect to lattice parameter §20.10(i)
  • modular transformations §20.7(viii)
  • multidimensional, see Chapter 21.
  • Neville’s §20.1, §22.2
  • nome §20.1
    • rectangular case §20.1
    • transformation of §20.7(iv), §20.7(ix)
  • notation §20.1
  • periodicity §20.2(ii)
  • permutation symmetry §20.11(v)
  • power series §20.6
  • quasi-periodicity §20.2(ii)
  • Ramanujan’s §20.11(ii)
  • Ramanujan’s change of base §20.11(iii)
  • rectangular case §20.1
  • relations to other functions
    • Dedekind’s eta function Figure 20.3.2, Figure 20.3.2, Figure 20.3.2
    • elliptic integrals §20.9(i)
    • elliptic modular function §20.9(ii)
    • Jacobi’s epsilon function §22.16(ii)
    • Jacobian elliptic functions §20.9(ii), §22.2
    • modular functions §23.15—§23.15(ii)
    • Riemann zeta function §20.9(iii)
    • symmetric elliptic integrals §19.25(iv)
    • Weierstrass elliptic functions §20.9(ii), §23.6(i)
  • Riemann §21.2(i)
  • Riemann with characteristics §21.2(ii)
  • sums of squares §20.7(i)
  • tables §20.15
  • translation by half-periods §20.2(iii)
  • values at $z=0$ §20.4—§20.4(ii)
  • Watson’s expansions §20.8
  • Watson’s identities §20.7(v)
  • with characteristics §20.11(iv)
  • zeros §20.2(iv)
• Thomae transformation
  • ${}_3{}^{}F_2^{}$ functions of matrix argument §35.8(iii)
• $3j$ symbols
  • relations to other functions
    • dual Hahn polynomials §18.38(iii)
    • Hahn polynomials §18.38(iii)
• $\mathit{3}j,\mathit{6}j,\mathit{9}j$ symbols
  • relation to generalized hypergeometric functions §16.24(iii), §16.4(iii), §16.4(iii)
• $\mathit{3}j$ symbols §34.2
  • angular momenta §34.2
  • applications §34.12
  • approximations for large parameters §34.8
  • computation §34.13
  • definition §34.2
  • Gaunt coefficient §34.3(vii)
  • Gaunt’s integral §34.3(vii)
  • generating functions §34.3(v)
  • graphical method §34.9
  • notation §34.1
  • orthogonality §34.3(iv)
  • projective quantum numbers §34.2
  • recursion relations §34.3(iii)
  • Regge symmetries §34.3(ii)
  • relations to other functions
    • Legendre functions §34.3(vii)
    • rotation matrices §34.3(vii)
    • spherical harmonics §34.3(vii)
  • representation as
    • finite sum of algebraic quantities §34.2
    • generalized hypergeometric functions §34.2
  • special cases §34.3(i)
  • summation convention §34.3(iv)
  • sums §34.3(vi)
  • symmetry §34.3(ii)
  • tables §34.14
  • triangle conditions §34.2
  • zeros §34.10

• Toda equation
  • Hermite polynomials §18.38(ii)
• tomography
  • confluent hypergeometric functions §13.28(iii)
• tops
  • Jacobian elliptic, or hyperelliptic, integrals §22.19(iv)
• toroidal coordinates §14.19(i), §14.31(i)
• toroidal functions §14.19(i)
  • applications §14.31(i)
  • definitions §14.19(i)
  • hypergeometric representations §14.19(ii)
  • integral representations §14.19(iii)
  • sums §14.19(iv)
  • Whipple’s formula §14.19(v)
• torus
  • complex §20.12(ii)
• transcendental equations
  • asymptotic solutions §2.2
• transcendental functions §32.2(i)
• transition points §2.8(i), §2.9(iii)
• transport equilibrium
  • generalized exponential integral §8.24(iii)
• triangle conditions
  • $\mathit{3}j$ symbols §34.2
• triangle inequality §1.9(i)
• triangles
  • solution of §4.42
• triangular matrices
  • confluent hypergeometric functions §13.27—§13.27
• triconfluent Heun equation §31.12
• trigonometric functions Ch.4
  • addition formulas §4.21(i)
  • analytic properties §4.14
  • applications
    • cubic equations §4.43
    • solution of triangles and spherical triangles §4.42
  • approximations §4.47
  • Chebyshev-series expansions §4.47(i)
  • computation §4.45(i)
  • conformal maps Figure 4.15.7, Figure 4.15.7, Figure 4.15.7
  • continued fractions §4.25
  • definitions §4.14
  • derivatives §4.20
  • differential equations §4.20
  • elementary properties §4.16—§4.16
  • graphics
    • complex argument §4.15(iii)—§4.15(iii)
    • real argument §4.15(i)
  • identities §4.21
  • inequalities §4.18
  • infinite products §4.22
  • integrals
    • definite §4.26(iii)
    • indefinite §4.26(ii)
  • inverse, see inverse trigonometric functions.
  • Laurent series §4.19
  • limits §4.17
  • Maclaurin series §4.19
  • moduli §4.21(iv)
  • multiples of argument §4.21(iii)
  • notation §4.1
  • orthogonality §4.26(iii)
  • partial fractions §4.22
  • periodicity §4.14
  • poles §4.28
  • real and imaginary parts §4.21(iv)
  • relations to hyperbolic functions §4.28
  • special values Table 4.17.1
  • squares and products §4.21(ii)
  • sums §4.27
  • tables §4.46
  • zeros §4.14
• triple integrals §1.5(v)
• truncated exponential series §8.11(v)
• turning points §2.8(i), §2.9(iii)
  • fractional or multiple §2.8(v)
• two-body relativistic scattering
  • Lamé polynomials §29.19(ii)

Index S Index U

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