.世界杯买球怎么买_『wn4.com_』2018世界杯一共多少支球队_w6n2c9o_2022年11月29日6时48分9秒_ok040qquy_gov_hk

(0.002 seconds)

31—40 of 799 matching pages

31: 3.6 Linear Difference Equations

… ►Given numerical values of

w_{0}

and

w_{1}

, the solution

w_{n}

of the equation …These errors have the effect of perturbing the solution by unwanted small multiples of

w_{n}

and of an independent solution

g_{n}

, say. … ►The unwanted multiples of

g_{n}

now decay in comparison with

w_{n}

, hence are of little consequence. … ►The latter method is usually superior when the true value of

w_{0}

is zero or pathologically small. … ►beginning with

e_{0}=w_{0}

. …

32: 19.29 Reduction of General Elliptic Integrals

… ►Let …where … ►Next, for

j=1,2

, define

Q_{j}(t)=f_{j}+g_{j}t+h_{j}t^{2}

, and assume both

Q

’s are positive for

y<t<x

. …where …If

Q_{1}(t)=(a_{1}+b_{1}t)(a_{2}+b_{2}t)

, where both linear factors are positive for

y<t<x

, and

Q_{2}(t)=f_{2}+g_{2}t+h_{2}t^{2}

, then (19.29.25) is modified so that …

33: Bibliography F

… ►

V. N. Faddeyeva and N. M. Terent’ev (1961) Tables of Values of the Function

w(z)=e^{-z^{2}}(1+2i\pi^{-1/2}\int_{0}^{z}e^{t^{2}}dt)

for Complex Argument. Edited by V. A. Fok; translated from the Russian by D. G. Fry. Mathematical Tables Series, Vol. 11, Pergamon Press, Oxford.

ⓘ

External Links:: MathReview, ZentralBlatt
Referenced by:: V. N. Faddeeva and N. M. Terent’ev (1954).
Encodings:: BibTeX

… ►

N. Fleury and A. Turbiner (1994) Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.

ⓘ

External Links:: ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt
Referenced by:: §13.3(ii), §15.5(i), §16.3(i).
Encodings:: BibTeX

… ►

A. S. Fokas and M. J. Ablowitz (1982) On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.

ⓘ

External Links:: ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt
Referenced by:: §32.13(i), §32.7(i), §32.7(iii).
Encodings:: BibTeX

… ►

P. J. Forrester and N. S. Witte (2004) Application of the

\tau

-function theory of Painlevé equations to random matrices:

\rm P_{\rm VI}

, the JUE, CyUE, cJUE and scaled limits. Nagoya Math. J. 174, pp. 29–114.

ⓘ

External Links:: ISSN 0027-7630, MathReview, ZentralBlatt
Referenced by:: §32.10(vi), §32.6(v).
Encodings:: BibTeX

… ►

L. W. Fullerton (1972) Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

ⓘ

Notes:: Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.
External Links:: ISSN 0001-0782, Document, Remark
Referenced by:: §8.28(ii).
Encodings:: BibTeX

…

Harvard University (1945) tabulates the real and imaginary parts of $h_{1}(z)$ , $h_{1}^{\prime}(z)$ , $h_{2}(z)$ , $h_{2}^{\prime}(z)$ for $-x_{0}\leq\Re z\leq x_{0}$ , $0\leq\Im z\leq y_{0}$ , $|x_{0}+iy_{0}|<6.1$ , with interval 0.1 in $\Re z$ and $\Im z$ . Precision is 8D. Here $h_{1}(z)=-2^{4/3}3^{1/6}i\operatorname{Ai}\left(e^{-\pi i/3}z\right)$ , $h_{2}(z)=2^{4/3}3^{1/6}i\operatorname{Ai}\left(e^{\pi i/3}z\right)$ .

… ►

•

Sherry (1959) tabulates $a_{k}$ , $\operatorname{Ai}'\left(a_{k}\right)$ , $a^{\prime}_{k}$ , $\operatorname{Ai}\left(a^{\prime}_{k}\right)$ , $k=1(1)50$ ; 20S.

… ►

•

National Bureau of Standards (1958) tabulates $A_{0}(x)\equiv\pi\operatorname{Hi}\left(-x\right)$ and $-A_{0}^{\prime}(x)\equiv\pi\operatorname{Hi}'\left(-x\right)$ for $x=0(.01)1(.02)5(.05)11$ and $1/x=0.01(.01)0.1$ ; $\int_{0}^{x}A_{0}(t)\,\mathrm{d}t$ for $x=0.5,1(1)11$ . Precision is 8D.

►

•

Nosova and Tumarkin (1965) tabulates $e_{0}(x)\equiv\pi\operatorname{Hi}\left(-x\right)$ , $e^{\prime}_{0}(x)=-\pi\operatorname{Hi}'\left(-x\right)$ , $\widetilde{e}_{0}(-x)\equiv-\pi\operatorname{Gi}\left(x\right)$ , $\widetilde{e}^{\mspace{2.0mu}\prime}_{0}(-x)=\pi\operatorname{Gi}'\left(x\right)$ for $x=-1(.01)10$ ; 7D. Also included are the real and imaginary parts of $e_{0}(z)$ and $ie^{\prime}_{0}(z)$ , where $z=iy$ and $y=0(.01)9$ ; 6-7D.

►

•

Gil et al. (2003c) tabulates the only positive zero of $\operatorname{Gi}'\left(z\right)$ , the first 10 negative real zeros of $\operatorname{Gi}\left(z\right)$ and $\operatorname{Gi}'\left(z\right)$ , and the first 10 complex zeros of $\operatorname{Gi}\left(z\right)$ , $\operatorname{Gi}'\left(z\right)$ , $\operatorname{Hi}\left(z\right)$ , and $\operatorname{Hi}'\left(z\right)$ . Precision is 11 or 12S.

…

35: 26.10 Integer Partitions: Other Restrictions

… ►

p_{m}\left(\mathcal{D},n\right)

denotes the number of partitions of

n

into at most

m

distinct parts. …The set

\{n\geq 1\>|\>n\equiv\pm j\ \pmod{k}\}

is denoted by

A_{j,k}

. … ►It is known that for

k>3

p\left(\mathcal{D}k,n\right)\geq p\left(\in\!A_{1,k+3},n\right)

, with strict inequality for

n

sufficiently large, provided that

k=2^{m}-1,m=3,4,5

, or

k\geq 32

; see Yee (2004). … ►where

I_{1}\left(x\right)

is the modified Bessel function (§10.25(ii)), and …The quantity

A_{k}(n)

is real-valued. …

36: 24.12 Zeros

… ►For the interval

\tfrac{1}{2}\leq x<\infty

denote the zeros of

B_{n}\left(x\right)

x_{j}^{(n)}

j=1,2,\dotsc

, with … ►Let

R(n)

be the total number of real zeros of

B_{n}\left(x\right)

. … ►For the interval

\frac{1}{2}\leq x<\infty

denote the zeros of

E_{n}\left(x\right)

y^{(n)}_{j}

j=1,2,\dotsc

, with … ►When

n

is odd

y^{(n)}_{1}=\tfrac{1}{2}

, … ►

B_{n}\left(x\right)

n=1,2,\dotsc

, has no multiple zeros. …

37: Bibliography B

… ►

R. Barakat (1961) Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

ⓘ

External Links:: FullText, MathReview (J. C. P. Miller), ZentralBlatt
Referenced by:: §8.7.
Encodings:: BibTeX

… ►

B. C. Berndt, S. Bhargava, and F. G. Garvan (1995) Ramanujan’s theories of elliptic functions to alternative bases. Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.

ⓘ

External Links:: ISSN 0002-9947, FullText, MathReview (J. Borwein), ZentralBlatt
Referenced by:: §15.8(v), §20.11(iii).
Encodings:: BibTeX

… ►

F. Bethuel (1998) Vortices in Ginzburg-Landau Equations. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), pp. 11–19.

ⓘ

External Links:: ISSN 1431-0643, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §17.17.
Encodings:: BibTeX

… ►

A. Bhattacharyya and L. Shafai (1988) Theoretical and experimental investigation of the elliptical annual ring antenna. IEEE Trans. Antennas and Propagation 36 (11), pp. 1526–1530.

ⓘ

External Links:: Document
Referenced by:: 5th item.
Encodings:: BibTeX

… ►

R. L. Bishop (1981) Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).

ⓘ

External Links:: ISSN 0035-9149, Document, MathReview
Referenced by:: Sidebar 9.SB1.
Encodings:: BibTeX

…

38: 5.10 Continued Fractions

… ►where ►

a_{0}=\tfrac{1}{12},

►

a_{1}=\tfrac{1}{30},

►

a_{2}=\tfrac{53}{210},

… ►For exact values of

a_{7}

a_{11}

and 40S values of

a_{0}

a_{40}

, see Char (1980). …

39: 34.3 Basic Properties: $\mathit{3j}$ Symbol

… ►When any one of

j_{1},j_{2},j_{3}

is equal to

0,\tfrac{1}{2}

, or

1

, the

\mathit{3j}

symbol has a simple algebraic form. …For these and other results, and also cases in which any one of

j_{1},j_{2},j_{3}

\frac{3}{2}

2

, see Edmonds (1974, pp. 125–127). … ►Even permutations of columns of a

\mathit{3j}

symbol leave it unchanged; odd permutations of columns produce a phase factor

(-1)^{j_{1}+j_{2}+j_{3}}

, for example, … ►Similar conventions apply to all subsequent summations in this chapter. … ►For the polynomials

P_{l}

see §18.3, and for the function

Y_{{l},{m}}

see §14.30. …

40: 28.8 Asymptotic Expansions for Large $q$

… ►Also let

\xi=2\sqrt{h}\cos x

and

D_{m}\left(\xi\right)=e^{-\ifrac{\xi^{2}}{4}}\mathit{He}_{m}\left(\xi\right)

(§18.3). … ►

\sigma_{m}\sim 1+\dfrac{s}{2^{3}h}+\dfrac{4s^{2}+3}{2^{7}h^{2}}+\dfrac{19s^{3}% +59s}{2^{11}h^{3}}+\cdots,

… ►

28.8.11

P_{m}(x)\sim 1+\dfrac{s}{2^{3}h{\cos}^{2}x}+\dfrac{1}{h^{2}}\left(\dfrac{s^{4}% +86s^{2}+105}{2^{11}{\cos}^{4}x}-\dfrac{s^{4}+22s^{2}+57}{2^{11}{\cos}^{2}x}% \right)+\cdots,

ⓘ

Defines:: $P_{m}(x)$ (locally)
Symbols:: $\sim$ : Poincaré asymptotic expansion, $\cos\NVar{z}$ : cosine function, $m$ : integer, $h$ : parameter and $x$ : real variable
A&S Ref:: 20.9.14 (in different form)
Permalink:: http://dlmf.nist.gov/28.8.E11
Encodings:: pMML, png, TeX
See also:: Annotations for §28.8(iii), §28.8 and Ch.28

… ►The approximations are expressed in terms of Whittaker functions

W_{\kappa,\mu}\left(z\right)

and

M_{\kappa,\mu}\left(z\right)

with

\mu=\tfrac{1}{4}

; compare §2.8(vi). … ►Subsequently the asymptotic solutions involving either elementary or Whittaker functions are identified in terms of the Floquet solutions

\operatorname{me}_{\nu}\left(z,q\right)

(§28.12(ii)) and modified Mathieu functions

{\operatorname{M}^{(j)}_{\nu}}\left(z,h\right)

(§28.20(iii)). …

.世界杯 买球怎么买_『wn4.com_』2018世界杯一共多少支球队_w6n2c9o_2022年11月29日6时48分9秒_ok040qquy_gov_hk