.韩国兰芝岛世界杯公园_『网址:687.vii』篮球世界杯竞猜_b5p6v3_pr7bnb1nb.com

SearchAdvancedHelp

The terms "pr7bnb1nb.com", "b5p6v3" were not found.Possible alternative term: "caniuse.com".

(0.007 seconds)

1—10 of 773 matching pages

1: 19.2 Definitions

… ►where $p_j$ is a polynomial in $t$ while $\rho$ and $\sigma$ are rational functions of $t$. … ►Here $a,b,p$ are real parameters, and $k_c$ and $x$ are real or complex variables, with $p\ne 0$, $k_c\ne 0$. … ►If , then $k_c$ is pure imaginary. … ►

§19.2(iv) A Related Function: $R_C(x,y)$

… ►For the special cases of $R_C(x,x)$ and $R_C(0,y)$ see (19.6.15). …

2: 25.21 Software

… ►

§25.21(vii) Fermi–Dirac and Bose–Einstein Integrals

…

3: 8.28 Software

… ►

§8.28(vii) Generalized Exponential Integral for Complex Argument and/or Parameter

…

4: 10.74 Methods of Computation

… ►In the case of the modified Bessel function $K_{\nu }\left(z\right)$ see especially Temme (1975). … ►It should be noted, however, that there is a difficulty in evaluating the coefficients $A_k(\zeta )$, $B_k(\zeta )$, $C_k(\zeta )$, and $D_k(\zeta )$, from the explicit expressions (10.20.10)–(10.20.13) when $z$ is close to $1$ owing to severe cancellation. … ►Similarly, to maintain stability in the interval the integration direction has to be forwards in the case of $I_{\nu }\left(x\right)$ and backwards in the case of $K_{\nu }\left(x\right)$, with initial values obtained in an analogous manner to those for $J_{\nu }\left(x\right)$ and $Y_{\nu }\left(x\right)$. … ►Then $J_n\left(x\right)$ and $Y_n\left(x\right)$ can be generated by either forward or backward recurrence on $n$ when , but if $n>x$ then to maintain stability $J_n\left(x\right)$ has to be generated by backward recurrence on $n$, and $Y_n\left(x\right)$ has to be generated by forward recurrence on $n$. … ►

§10.74(vii) Integrals

…

5: 33.23 Methods of Computation

… ►§33.8 supplies continued fractions for $F_{\mathrm{\ell }}^{\prime }/F_{\mathrm{\ell }}$ and $H_{\mathrm{\ell }}^{\pm }{}_{}{}^{\prime }/H_{\mathrm{\ell }}^{\pm }$. Combined with the Wronskians (33.2.12), the values of $F_{\mathrm{\ell }}$, $G_{\mathrm{\ell }}$, and their derivatives can be extracted. … ►Bardin et al. (1972) describes ten different methods for the calculation of $F_{\mathrm{\ell }}$ and $G_{\mathrm{\ell }}$, valid in different regions of the ($\eta ,\rho$)-plane. … ►

§33.23(vii) WKBJ Approximations

… ►Hull and Breit (1959) and Barnett (1981b) give WKBJ approximations for $F_0$ and $G_0$ in the region inside the turning point: .

6: 18.30 Associated OP’s

… ►where $p_n(x;c)$ is given by (18.30.2) and (18.30.3), with $A_n$, $B_n$, and $C_n$ as in (18.9.2). …where the generalized hypergeometric function ${}_4{}^{}F_3^{}$ is defined by (16.2.1). ►For corresponding corecursive associated Jacobi polynomials, corecursive associated polynomials being discussed in §18.30(vii), see Letessier (1995). … ► $F(z)$ and $F_n(z)$ of (18.30.23) and (18.30.24) are, also, precisely those of (18.2.34) and (18.2.35), now expressed via the traditional, $A_n$, $B_n$, $C_n$ coefficients, rather than the monic, ${\alpha }_n$, ${\beta }_n$, recursion coefficients. … ►

§18.30(vii) Corecursive and Associated Monic Orthogonal Polynomials

…

7: 8.21 Generalized Sine and Cosine Integrals

… ►For ${𝗃}_n\left(z\right)$ see §10.47(ii). … ►

§8.21(vii) Auxiliary Functions

… ►

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

ⓘ

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

►

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

ⓘ

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

… ►

8.21.24 $$f(a,z)=\frac{z^a}{2}{\int }_0^{\mathrm{\infty }}\left({(1+\mathrm{i}t)}^{a-1}+{(1-\mathrm{i}t)}^{a-1}\right){\mathrm{e}}^{-zt}dt,$$

ⓘ

Symbols:

$dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\int$: integral, $z$: complex variable, $a$: parameter and $f(a,z)$: auxiliary function

Referenced by:

§8.21(vii), §8.21(viii)

Permalink:

http://dlmf.nist.gov/8.21.E24

Encodings:

pMML, png, TeX

See also:

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

…

8: 18.16 Zeros

… ►Let $j_{\alpha ,m}$ be the $m$th positive zero of the Bessel function $J_{\alpha }\left(x\right)$ (§10.21(i)). … ►Let ${\varphi }_m=j_{\alpha ,m}/\rho$. … ►For $m=1,2,\mathrm{\dots },n$, and with $j_{\alpha ,m}$ as in §18.16(ii), … ►In the notation of this reference $x_{n,m}=u_{a,m}$, $\mu =\sqrt{2n+1}$, and $\alpha ={\mu }^{-\frac{4}{3}}{a}_m$. … ►

§18.16(vii) Discriminants

…

9: Bibliography I

… ►

Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines. Z. Angew. Math. Mech. 75 (12), pp. 917–926.

ⓘ

External Links:

ISSN 0044-2267, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

… ►

Highly Oscillatory Quadrature: The Story So Far. In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.), pp. 97–118.

ⓘ

Notes:

Proceedings of ENuMath, Santiago de Compostela (2005)

External Links:

ISBN 3-540-34287-7, MathReview, ZentralBlatt

Referenced by:

§3.5(vii).

Encodings:

BibTeX

… ►

$q$-Hermite polynomials, biorthogonal rational functions, and $q$-beta integrals. Trans. Amer. Math. Soc. 346 (1), pp. 63–116.

ⓘ

External Links:

ISSN 0002-9947, FullText, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.28(vii).

Encodings:

BibTeX

… ►

Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

ⓘ

Notes:

With two chapters by Walter Van Assche, With a foreword by Richard A. Askey, Corrected reprint of the 2005 original.

External Links:

ISBN 978-0-521-14347-9, MathReview Entry, ZentralBlatt

Referenced by:

§18.12, (18.15.4_5), (18.16.19), (18.16.20), (18.16.21), §18.17(ii), §18.18(vii), §18.19, (18.2.20), §18.2(vi), §18.2(xii), §18.2(xii), §18.2(x), §18.20(i), §18.20(ii), §18.21(ii), §18.22(i), §18.22(ii), §18.22(iii), §18.23, §18.25(i), §18.25(iii), §18.26(i), §18.26(iv), (18.27.4), §18.27(i), §18.27(ii), §18.27(iii), §18.27(v), §18.27(vi), §18.28(i), §18.28(ii), §18.28(iii), §18.28(v), §18.28(vi), §18.28(vii), §18.28(viii), §18.30(vi), §18.30(vii), §18.30(iii), §18.30(iv), §18.30, §18.30(vi), §18.34(i), §18.34(ii), §18.34(ii), §18.34(iii), (18.35.4), (18.35.5), (18.35.6), (18.35.6_2), (18.35.6_3), (18.35.6_4), (18.35.7), (18.35.8), §18.35(ii), §18.35(iii), §18.36(iii), §18.38(ii), §18.39(iv), §18.39(iv), §18.39(iv), (18.40.4), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

Encodings:

BibTeX

… ►

From Gauss to Painlevé: A Modern Theory of Special Functions. Aspects of Mathematics E, Vol. 16, Friedr. Vieweg & Sohn, Braunschweig, Germany.

ⓘ

External Links:

ISBN 3-528-06355-6, MathReview (Takeshi Sasaki), ZentralBlatt

Referenced by:

§32.2(vi), §32.7(vii).

Encodings:

BibTeX

10: 1.10 Functions of a Complex Variable

… ►Let $f_1(z)$ be analytic in a domain $D_1$. … ►Then … ►

§1.10(vii) Inverse Functions

… ►Suppose that …Let $w_0=f(z_0)$. …