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Notations T

*ABCDEFGHIJKLMNOPQRS♦T♦UVWXYZ
T n
tangent numbers; §24.15(ii)
T n ( x )
Chebyshev polynomial of the first kind; Table 18.3.1
T n * ( x )
shifted Chebyshev polynomial of the first kind; Table 18.3.1
tan z
tangent function; 4.14.4
tanh z
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 ) = θ 3 ( 0 , x )
alternative notation; 27.13.4
(with θj(z,q): theta function)
θ ν ( x )
phase of Bessel functions; 10.18.3
θ j ( z | τ )
theta function; §20.2(i)
θ j ( z , q )
theta function; §20.2(i)
Θ ( ϕ | B ) = θ ( ϕ / ( 2 π i ) | B / ( 2 π i ) )
notation used by Belokolos et al. (1994), Dubrovin (1981); §21.1
(with θ(z|Ω): Riemann theta function)
Θ ( z | τ ) = θ 4 ( u | τ )
Jacobi’s notation; §20.1
(with θj(z|τ): theta function)
θ ( z | Ω )
Riemann theta function; 21.2.1
Θ 1 ( z | τ ) = θ 3 ( u | τ )
Jacobi’s notation; §20.1
(with θj(z|τ): theta function)
ϑ j ( z | τ ) = θ j ( π z | τ )
notation used by McKean and Moll (1999, p. 125); §20.1
(with θj(z|τ): theta function)
θ c ( z | τ ) = θ 2 ( u | τ ) / θ 2 ( 0 | τ )
notation used by Neville (1951); §20.1
(with θj(z|τ): theta function)
θ d ( z | τ ) = θ 3 ( u | τ ) / θ 3 ( 0 | τ )
notation used by Neville (1951); §20.1
(with θj(z|τ): theta function)
θ n ( z | τ ) = θ 4 ( u | τ ) / θ 4 ( 0 | τ )
notation used by Neville (1951); §20.1
(with θj(z|τ): theta function)
θ s ( z | τ ) = π θ 3 2 ( 0 | τ ) θ 1 ( u | τ ) / θ 1 ( 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 [ α β ] ( z | Ω )
Riemann theta function with characteristics; 21.2.5
tr A
trace of matrix A; Common Notations and Definitions