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1: 4.46 Tables
This handbook also includes lists of references for earlier tables, as do Fletcher et al. (1962) and Lebedev and Fedorova (1960). …
2: 7.23 Tables
  • Fettis et al. (1973) gives the first 100 zeros of erf z and w ( z ) (the table on page 406 of this reference is for w ( z ) , not for erfc z ), 11S.

  • Zhang and Jin (1996, p. 642) includes the first 10 zeros of erf z , 9D; the first 25 distinct zeros of C ( z ) and S ( z ) , 8S.

  • 3: 36.7 Zeros
    The zeros in Table 36.7.1 are points in the x = ( x , y ) plane, where ph Ψ 2 ( x ) is undetermined. …
    Table 36.7.1: Zeros of cusp diffraction catastrophe to 5D.
    Zeros { x y } inside, and zeros [ x y ] outside, the cusp x 2 = 8 27 | y | 3 .
    4: 7.13 Zeros
    Table 7.13.1: Zeros x n + i y n of erf z .
    n x n y n
    Table 7.13.2: Zeros x n + i y n of erfc z .
    n x n y n
    Table 7.13.3: Complex zeros x n + i y n of C ( z ) .
    n x n y n
    Table 7.13.4: Complex zeros x n + i y n of S ( z ) .
    n x n y n
    5: 28.35 Tables
    §28.35(iii) Zeros
    6: 9.18 Tables
    §9.18(iv) Zeros
  • Nosova and Tumarkin (1965) tabulates e 0 ( x ) π Hi ( - x ) , e 0 ( x ) = - π Hi ( - x ) , e ~ 0 ( - x ) - π Gi ( x ) , e ~ 0 ( - x ) = π Gi ( x ) for x = - 1 ( .01 ) 10 ; 7D. Also included are the real and imaginary parts of e 0 ( z ) and i e 0 ( z ) , where z = i y and y = 0 ( .01 ) 9 ; 6-7D.

  • Gil et al. (2003c) tabulates the only positive zero of Gi ( z ) , the first 10 negative real zeros of Gi ( z ) and Gi ( z ) , and the first 10 complex zeros of Gi ( z ) , Gi ( z ) , Hi ( z ) , and Hi ( z ) . Precision is 11 or 12S.

  • 7: 9.9 Zeros
    §9.9(v) Tables
    Table 9.9.1: Zeros of Ai and Ai .
    k a k Ai ( a k ) a k Ai ( a k )
    Table 9.9.3: Complex zeros of Bi .
    e - π i / 3 β k Bi ( β k )
    Table 9.9.4: Complex zeros of Bi .
    e - π i / 3 β k Bi ( β k )
    8: 3.5 Quadrature
    Table 3.5.2: Nodes and weights for the 10-point Gauss–Legendre formula.
    ± x k w k
    Table 3.5.3: Nodes and weights for the 20-point Gauss–Legendre formula.
    ± x k w k
    Table 3.5.4: Nodes and weights for the 40-point Gauss–Legendre formula.
    ± x k w k
    Table 3.5.5: Nodes and weights for the 80-point Gauss–Legendre formula.
    ± x k w k
    Table 3.5.6: Nodes and weights for the 5-point Gauss–Laguerre formula.
    x k w k
    9: 10.75 Tables
    §10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives
  • Döring (1966) tabulates all zeros of Y 0 ( z ) , Y 1 ( z ) , H 0 ( 1 ) ( z ) , H 1 ( 1 ) ( z ) , that lie in the sector | z | < 158 , | ph z | π , to 10D. Some of the smaller zeros of Y n ( z ) and H n ( 1 ) ( z ) for n = 2 , 3 , 4 , 5 , 15 are also included.

  • §10.75(vi) Zeros of Modified Bessel Functions and their Derivatives
  • Zhang and Jin (1996, pp. 296–305) tabulates j n ( x ) , j n ( x ) , y n ( x ) , y n ( x ) , i n ( 1 ) ( x ) , i n ( 1 ) ( x ) , k n ( x ) , k n ( x ) , n = 0 ( 1 ) 10 ( 10 ) 30 , 50, 100, x = 1 , 5, 10, 25, 50, 100, 8S; x j n ( x ) , ( x j n ( x ) ) , x y n ( x ) , ( x y n ( x ) ) (Riccati–Bessel functions and their derivatives), n = 0 ( 1 ) 10 ( 10 ) 30 , 50, 100, x = 1 , 5, 10, 25, 50, 100, 8S; real and imaginary parts of j n ( z ) , j n ( z ) , y n ( z ) , y n ( z ) , i n ( 1 ) ( z ) , i n ( 1 ) ( z ) , k n ( z ) , k n ( z ) , n = 0 ( 1 ) 15 , 20(10)50, 100, z = 4 + 2 i , 20 + 10 i , 8S. (For the notation replace j , y , i , k by j , y , i ( 1 ) , k , respectively.)

  • §10.75(xi) Kelvin Functions and their Derivatives
    10: 5.4 Special Values and Extrema
    §5.4(iii) Extrema