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Notations

Notations T

T n
tangent numbers; §24.15(ii)
T ( z )
Tree T-function; §4.13
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 ( x ) = θ 3 ( 0 , x )
alternative notation; (27.13.4)
(with θj(z,q): theta function)
θ ( z )
Airy phase function; (9.8.4)
θ ν ( x )
phase of Bessel functions; (10.18.3)
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, π: the ratio of the circumference of a circle to its diameter and i: imaginary unit)
θ ( 𝐳 | 𝛀 )
Riemann theta function; (21.2.1)
Θ ( z | τ ) = θ 4 ( u | τ )
Jacobi’s notation; §20.1
(with θj(z|τ): theta function)
Θ 1 ( z | τ ) = θ 3 ( u | τ )
Jacobi’s notation; §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 ^ ( 𝐳 | 𝛀 )
scaled Riemann theta function; (21.2.2)
θ j ( z , q )
theta function; §20.2(i)
θ j ( z | τ )
theta function; §20.2(i)
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 and π: the ratio of the circumference of a circle to its diameter)
θ ( η , ρ )
phase of Coulomb functions; (33.2.9)
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 and π: the ratio of the circumference of a circle to its diameter)
θ [ 𝜶 𝜷 ] ( 𝐳 | 𝛀 )
Riemann theta function with characteristics; (21.2.5)
tr 𝐀
trace of matrix; Common Notations and Definitions