.世界杯广告词吃的_『网址:687.vii』2019蓝男世界杯杯_b5p6v3_g8ms0qwso

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11: 34.9 Graphical Method

… ►For an account of this method see Brink and Satchler (1993, Chapter VII). …

12: 34.13 Methods of Computation

… ►A review of methods of computation is given in Srinivasa Rao and Rajeswari (1993, Chapter VII, pp. 235–265). …

13: Errata

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Version 1.0.25 (December 15, 2019)

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Version 1.0.24 (September 15, 2019)

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Version 1.0.23 (June 15, 2019)

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Version 1.0.22 (March 15, 2019)

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Some references were added to §§7.25(ii), 7.25(iii), 7.25(vi), 8.28(ii), and to ¶Products (in §10.74(vii)) and §10.77(ix).

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14: 10.74 Methods of Computation

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§10.74(vii) Integrals

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15: 33.23 Methods of Computation

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§33.23(vii) WKBJ Approximations

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16: 14.32 Methods of Computation

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Application of the uniform asymptotic expansions for large values of the parameters given in §§14.15 and 14.20(vii)–14.20(ix).

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17: 8.21 Generalized Sine and Cosine Integrals

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§8.21(vii) Auxiliary Functions

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8.21.18 $$f(a,z)=\mathrm{si}(a,z)\cos z-\mathrm{ci}(a,z)\sin z,$$

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Defines:

$f(a,z)$: auxiliary function (locally)

Symbols:

$\cos z$: cosine function, $\mathrm{ci}(a,z)$: generalized cosine integral, $\mathrm{si}(a,z)$: generalized sine integral, $\sin z$: sine function, $z$: complex variable and $a$: parameter

A&S Ref:

5.2.6 (This generalizes the form in AMS 55.)

Referenced by:

§8.21(vii)

Permalink:

http://dlmf.nist.gov/8.21.E18

Encodings:

pMML, png, TeX

See also:

Annotations for §8.21(vii), §8.21 and Ch.8

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8.21.19 $$g(a,z)=\mathrm{si}(a,z)\sin z+\mathrm{ci}(a,z)\cos z.$$

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Defines:

$g(a,z)$: auxiliary function (locally)

Symbols:

$\cos z$: cosine function, $\mathrm{ci}(a,z)$: generalized cosine integral, $\mathrm{si}(a,z)$: generalized sine integral, $\sin z$: sine function, $z$: complex variable and $a$: parameter

A&S Ref:

5.2.7 (This generalizes the form in AMS 55.)

Referenced by:

§8.21(vii)

Permalink:

http://dlmf.nist.gov/8.21.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §8.21(vii), §8.21 and Ch.8

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8.21.22 $$f(a,z)={\int }_0^{\mathrm{\infty }}\frac{\sin t}{{(t+z)}^{1-a}}dt,$$

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Symbols:

$dx$: differential of $x$ , $\int$: integral, $\sin z$: sine function, $z$: complex variable, $a$: parameter and $f(a,z)$: auxiliary function

A&S Ref:

5.2.12 (This generalizes the form in AMS 55.)

Referenced by:

§8.21(vii)

Permalink:

http://dlmf.nist.gov/8.21.E22

Encodings:

pMML, png, TeX

See also:

Annotations for §8.21(vii), §8.21 and Ch.8

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8.21.23 $$g(a,z)={\int }_0^{\mathrm{\infty }}\frac{\cos t}{{(t+z)}^{1-a}}dt.$$

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Symbols:

$\cos z$: cosine function, $dx$: differential of $x$ , $\int$: integral, $z$: complex variable, $a$: parameter and $g(a,z)$: auxiliary function

A&S Ref:

5.2.13 (This generalizes the form in AMS 55.)

Referenced by:

§8.21(vii)

Permalink:

http://dlmf.nist.gov/8.21.E23

Encodings:

pMML, png, TeX

See also:

Annotations for §8.21(vii), §8.21 and Ch.8

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18: 3.1 Arithmetics and Error Measures

… ►The current floating point arithmetic standard is IEEE 754-2019 IEEE (2019), a minor technical revision of IEEE 754-2008 IEEE (2008), which was adopted in 2011 by the International Standards Organization as ISO/IEC/IEEE 60559. …

19: DLMF Project News

error generating summary

20: 18.30 Associated OP’s

… ►For corresponding corecursive associated Jacobi polynomials, corecursive associated polynomials being discussed in §18.30(vii), see Letessier (1995). … ►

§18.30(vii) Corecursive and Associated Monic Orthogonal Polynomials

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18.30.27 $$x{\widehat{p}}_n(x;c)={\widehat{p}}_{n+1}(x;c)+{\alpha }_{n+c}{\widehat{p}}_n(x;c)+{\beta }_{n+c}{\widehat{p}}_{n-1}(x;c),$$ $n=1,2,\mathrm{\dots }$.

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Symbols:

$n$: nonnegative integer and $x$: real variable

Referenced by:

§18.30(vii), §18.30(vii), §18.30(vii)

Permalink:

http://dlmf.nist.gov/18.30.E27

Encodings:

pMML, png, TeX

See also:

Annotations for §18.30(vii), §18.30(vii), §18.30 and Ch.18

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18.30.29 $${\widehat{p}}_n^{(0)}(x)={\widehat{p}}_{n-1}(x;1)$$

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Symbols:

$n$: nonnegative integer and $x$: real variable

Permalink:

http://dlmf.nist.gov/18.30.E29

Encodings:

pMML, png, TeX

See also:

Annotations for §18.30(vii), §18.30(vii), §18.30 and Ch.18

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18.30.30 $${\widehat{p}}_n^{(k)}(x)={\widehat{p}}_{n-1}(x;k+1).$$

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Symbols:

$k$: nonnegative integer, $n$: nonnegative integer and $x$: real variable

Permalink:

http://dlmf.nist.gov/18.30.E30

Encodings:

pMML, png, TeX

See also:

Annotations for §18.30(vii), §18.30(vii), §18.30 and Ch.18

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