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1: 19.38 Approximations
Minimax polynomial approximations (§3.11(i)) for K ( k ) and E ( k ) in terms of m = k 2 with 0 m < 1 can be found in Abramowitz and Stegun (1964, §17.3) with maximum absolute errors ranging from 4×10⁻⁵ to 2×10⁻⁸. Approximations of the same type for K ( k ) and E ( k ) for 0 < k 1 are given in Cody (1965a) with maximum absolute errors ranging from 4×10⁻⁵ to 4×10⁻¹⁸. …
2: 3.1 Arithmetics and Error Measures
The lower and upper bounds for the absolute values of the nonzero machine numbers are given by … Also in this arithmetic generalized precision can be defined, which includes absolute error and relative precision (§3.1(v)) as special cases. … If x * is an approximation to a real or complex number x , then the absolute error is
3.1.8 ϵ a = | x * - x | .
3.1.9 ϵ r = | x * - x x | = ϵ a | x | .
3: 6.13 Zeros
Ci ( x ) and si ( x ) each have an infinite number of positive real zeros, which are denoted by c k , s k , respectively, arranged in ascending order of absolute value for k = 0 , 1 , 2 , . …
4: 23.16 Graphics
In Figures 23.16.2 and 23.16.3, height corresponds to the absolute value of the function and color to the phase. …
5: 5.3 Graphics
In the graphics shown in this subsection, both the height and color correspond to the absolute value of the function. …
6: 8.27 Approximations
  • DiDonato (1978) gives a simple approximation for the function F ( p , x ) = x - p e x 2 / 2 x e - t 2 / 2 t p d t (which is related to the incomplete gamma function by a change of variables) for real p and large positive x . This takes the form F ( p , x ) = 4 x / h ( p , x ) , approximately, where h ( p , x ) = 3 ( x 2 - p ) + ( x 2 - p ) 2 + 8 ( x 2 + p ) and is shown to produce an absolute error O ( x - 7 ) as x .

  • 7: 9.3 Graphics
    In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. …
    8: 14.22 Graphics
    In the graphics shown in this section, height corresponds to the absolute value of the function and color to the phase. …
    9: 4.3 Graphics
    In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase. …
    10: 7.13 Zeros
    erf z has a simple zero at z = 0 , and in the first quadrant of there is an infinite set of zeros z n = x n + i y n , n = 1 , 2 , 3 , , arranged in order of increasing absolute value. … In the sector 1 2 π < ph z < 3 4 π , erfc z has an infinite set of zeros z n = x n + i y n , n = 1 , 2 , 3 , , arranged in order of increasing absolute value. … In the first quadrant of C ( z ) has an infinite set of zeros z n = x n + i y n , n = 1 , 2 , 3 , , arranged in order of increasing absolute value. …