even part
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1—10 of 25 matching pages
1: 7.9 Continued Fractions
2: 1.12 Continued Fractions
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§1.12(iv) Contraction and Extension
… ►If , , then is called the even part of . The even 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. …3: 18.17 Integrals
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18.17.41
. Also, ,
even;
, odd.
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4: 28.23 Expansions in Series of Bessel Functions
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►When the series in the even-numbered equations converge for and , and the series in the odd-numbered equations converge for and .
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5: 20.1 Special Notation
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, | integers. |
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the nome, , . Since is not a single-valued function of , it is assumed that is known, even when is specified. Most applications concern the rectangular case , , so that and and are uniquely related. | |
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6: 19.38 Approximations
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►They are valid over parts of the complex and planes.
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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7: 4.37 Inverse Hyperbolic Functions
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4.37.11
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8: 14.17 Integrals
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14.17.15
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►(When is even the condition is not needed.)
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14.17.18
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14.17.19
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and .
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14.17.20
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9: 18.32 OP’s with Respect to Freud Weights
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►where is real, even, nonnegative, and continuously differentiable, where increases for , and as , see Freud (1969).
…See the early survey by Nevai (1986, Part 2).
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10: 37.15 Orthogonal Polynomials on the Ball
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37.15.20
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