fractional part
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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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2: 5.10 Continued Fractions
§5.10 Continued Fractions
►For , …3: 1.12 Continued Fractions
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§1.12(iv) Contraction and Extension
… ►The odd part of exists iff , , and up to equivalence is given by … ►and the even and odd parts of the continued fraction converge to finite values. …4: 1.15 Summability Methods
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►For and , the Riemann-Liouville fractional integral of order
is defined by
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1.15.48
, .
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►For , an integer, and , the fractional derivative of order is defined by
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5: 7.18 Repeated Integrals of the Complementary Error Function
6: 7.9 Continued Fractions
7: 5.9 Integral Representations
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, , and .
(The fractional powers have their principal values.)
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5.9.2_5
,
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5.9.3
, ,
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►For ,
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8: 5.12 Beta Function
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►In this section all fractional powers have their principal values, except where noted otherwise.
In (5.12.1)–(5.12.4) it is assumed and .
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►In (5.12.8) the fractional powers have their principal values when and , and are continued via continuity.
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►In (5.12.11) and (5.12.12) the fractional powers are continuous on the integration paths and take their principal values at the beginning.
…when , is not an integer and the contour cuts the real axis between and the origin.
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9: Wadim Zudilin
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►His research interests are primarily focused on applications of special functions in different parts of number theory.
Zudilin is author or coauthor of numerous publications including the book Neverending Fractions, An Introduction to Continued Fractions published by Cambridge University Press in 2014.
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