Digital Library of Mathematical Functions
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NIST
Notations

Notations T

*ABCDEFGHIJKLMNOPQRS♦T♦UVWXYZ
Tn
tangent numbers; 24.15(ii)
Tn(x)
Chebyshev polynomial of the first kind; 18.3.1
Tn*(x)
shifted Chebyshev polynomial of the first kind; 18.3.1
tanz
tangent function; (4.14.4)
tanhz
hyperbolic tangent function; (4.28.4)
τ(n)
Ramanujan’s tau function; (27.14.18)
θ(z)
Airy phase function; 9.8(i)
ϑ(x)=θ3(0,x)
alternative notation; (27.13.4)
(with θj(z,q): theta function)
θν(x)
phase of Bessel functions; (10.18.3)
θj(z|τ)
theta function; 20.2(i)
θj(z,q)
theta function; 20.2(i)
Θ(ϕ|B)=θ(ϕ/(2π)|B/(2π))
notation used by Belokolos et al. (1994), Dubrovin (1981); 21.1
(with θ(z|Ω): Riemann theta function)
Θ(z|τ)=θ4(u|τ)
Jacobi’s notation; 20.1
(with θj(z|τ): theta function)
θ(z|Ω)
Riemann theta function; (21.2.1)
Θ1(z|τ)=θ3(u|τ)
Jacobi’s notation; 20.1
(with θj(z|τ): theta function)
ϑj(z|τ)=θj(πz|τ)
notation used by McKean and Moll (1999, p. 125); 20.1
(with θj(z|τ): theta function)
θc(z|τ)=θ2(u|τ)/θ2(0|τ)
notation used by Neville (1951); 20.1
(with θj(z|τ): theta function)
θd(z|τ)=θ3(u|τ)/θ3(0|τ)
notation used by Neville (1951); 20.1
(with θj(z|τ): theta function)
θn(z|τ)=θ4(u|τ)/θ4(0|τ)
notation used by Neville (1951); 20.1
(with θj(z|τ): theta function)
θs(z|τ)=πθ32(0|τ)θ1(u|τ)/θ1(0|τ)
notation used by Neville (1951); 20.1
(with θj(z|τ): theta function)
θ(η,ρ)
phase of Coulomb functions; (33.2.9)
θ^(z|Ω)
scaled Riemann theta function; (21.2.2)
θ[αβ](z|Ω)
Riemann theta function with characteristics; (21.2.5)
trA
trace of matrix A; Common Notations and Definitions