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1: 3.1 Arithmetics and Error Measures
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►A nonzero normalized binary floating-point machine number
is represented as
…where is equal to or , each , , is either or , is the most significant bit, () is the number of significant bits , is the least significant bit, is an integer called the exponent, is the significand, and is the fractional
part.
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3.1.2
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►For given values of , , and , the format width in bits
of a computer word is the total number of bits: the sign (one bit), the significant bits ( bits), and the bits allocated to the exponent (the remaining bits).
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3.1.4
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2: 19.38 Approximations
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►The accuracy is controlled by the number of terms retained in the approximation; for real variables the number of significant figures appears to be roughly twice the number of terms retained, perhaps even for near with the improvements made in the 1970 reference.
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3: 6.16 Mathematical Applications
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§6.16(ii) Number-Theoretic Significance of
…4: Richard A. Askey
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►Another significant contribution was the Askey-Gasper inequality for Jacobi polynomials which was published in Positive Jacobi polynomial sums. II (with G.
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5: About Color Map
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►In doing this, however, we would like to place the mathematically significant phase values, specifically the multiples of correponding to the real and imaginary axes, at more immediately recognizable colors.
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6: 19.36 Methods of Computation
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►If (19.25.9) is used when , cancellations may lead to loss of significant figures when is close to 1 and , as shown by Reinsch and Raab (2000).
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can be evaluated by using (19.25.7), and by using (19.21.10), but cancellations may become significant.
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►Near these points there will be loss of significant figures in the computation of or .
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►This method loses significant figures in if and are nearly equal unless they are given exact values—as they can be for tables.
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7: Mathematical Introduction
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►05, and the corresponding function values are tabulated to 8 decimal places or 8 significant figures.
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or | half-closed intervals. |
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S | significant figures. |
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8: DLMF Project News
error generating summary9: 2.11 Remainder Terms; Stokes Phenomenon
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►If the results agree within
significant figures, then it is likely—but not certain—that the truncated asymptotic series will yield at least correct significant figures for larger values of .
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►In effect, (2.11.7) “corrects” (2.11.6) by introducing a term that is relatively exponentially small in the neighborhood of , is increasingly significant as passes from to , and becomes the dominant contribution after passes .
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10: Software Index
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►The following are web-based software repositories with significant holdings in the area of special functions.
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