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1: 32.11 Asymptotic Approximations for Real Variables
32.11.9 θ 0 = 3 2 d 2 ln 2 + ph Γ ( 1 - 1 2 i d 2 ) + 1 4 π ( 1 - 2 sign ( k ) ) ,
32.11.17 d 2 = π - 1 ln ( 1 + k 2 ) , sign ( k ) = ( - 1 ) n .
2: 1.16 Distributions
1.16.44 sign ( x ) = 2 H ( x ) - 1 , x 0 ,
1.16.45 sign = 2 H = 2 δ ,
3: 4.16 Elementary Properties
Table 4.16.1: Signs of the trigonometric functions in the four quadrants.
Quadrant sin θ , csc θ cos θ , sec θ tan θ , cot θ
Table 4.16.2: Trigonometric functions: quarter periods and change of sign.
x - θ 1 2 π ± θ π ± θ 3 2 π ± θ 2 π ± θ
4: 4.24 Inverse Trigonometric Functions: Further Properties
4.24.4 arctan z = ± π 2 - 1 z + 1 3 z 3 - 1 5 z 5 + , z 0 , | z | 1 .
5: 10.21 Zeros
For sign properties of the forward differences that are defined by … The zeros of the functions
§10.21(xiii) Rayleigh Function
6: Bibliography S
  • J. Steinig (1972) The sign of Lommel’s function. Trans. Amer. Math. Soc. 163, pp. 123–129.
  • 7: 28.12 Definitions and Basic Properties
    §28.12 Definitions and Basic Properties
    For change of signs of ν and q , …
    §28.12(ii) Eigenfunctions me ν ( z , q )
    For changes of sign of ν , q , and z , … For change of signs of ν and z , …
    8: 10.44 Sums
    If 𝒵 = I and the upper signs are taken, then the restriction on λ is unnecessary. …
    9: 4.37 Inverse Hyperbolic Functions
    §4.37 Inverse Hyperbolic Functions
    the upper/lower signs corresponding to the right/left sides. … the upper/lower sign corresponding to the upper/lower side. … the upper/lower sign corresponding to the upper/lower side. … the upper/lower sign corresponding to the upper/lower sides. …
    10: 33.2 Definitions and Basic Properties
    The function F ( η , ρ ) is recessive (§2.7(iii)) at ρ = 0 , and is defined by …The choice of ambiguous signs in (33.2.3) and (33.2.4) is immaterial, provided that either all upper signs are taken, or all lower signs are taken. … The functions H ± ( η , ρ ) are defined by … …
    §33.2(iv) Wronskians and Cross-Product