absolute
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1—10 of 46 matching pages
1: 19.38 Approximations
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►Minimax polynomial approximations (§3.11(i)) for and in terms of with 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 and for are given in Cody (1965a) with maximum absolute errors ranging from 4×10⁻⁵ to 4×10⁻¹⁸.
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2: 3.1 Arithmetics and Error Measures
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►The lower and upper bounds for the absolute values of the nonzero machine numbers are given by
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►Also in this arithmetic generalized precision can be defined, which includes absolute error and relative precision (§3.1(v)) as special cases.
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►If is an approximation to a real or complex number , then the absolute error is
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3.1.8
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3.1.9
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3: 6.13 Zeros
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and each have an infinite number of positive real zeros, which are denoted by , , respectively, arranged in ascending order of absolute value for .
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4: 23.16 Graphics
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►In Figures 23.16.2 and 23.16.3, height corresponds to the absolute value of the function and color to the phase.
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5: 4.3 Graphics
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►In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase.
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6: 5.3 Graphics
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►In the graphics shown in this subsection, both the height and color correspond to the absolute value of the function.
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7: 8.27 Approximations
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DiDonato (1978) gives a simple approximation for the function (which is related to the incomplete gamma function by a change of variables) for real and large positive . This takes the form , approximately, where and is shown to produce an absolute error as .
8: 9.3 Graphics
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►In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase.
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9: 14.22 Graphics
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►In the graphics shown in this section, height corresponds to the absolute value of the function and color to the phase.
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10: 7.13 Zeros
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has a simple zero at , and in the first quadrant of there is an infinite set of zeros , , arranged in order of increasing absolute value.
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►In the sector , has an infinite set of zeros , , arranged in order of increasing absolute value.
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►In the first quadrant of
has an infinite set of zeros , , arranged in order of increasing absolute value.
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