大学结业证书是什么学历〖办证V信ATV1819〗16d

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11—20 of 501 matching pages

11: 27.15 Chinese Remainder Theorem

… ►Choose four relatively prime moduli

m_{1},m_{2},m_{3}

, and

m_{4}

of five digits each, for example

2^{16}-3

2^{16}-1

2^{16}+1

, and

2^{16}+3

. …

12: Bibliography Y

… ►

G. D. Yakovleva (1969) Tables of Airy Functions and Their Derivatives. Izdat. Nauka, Moscow (Russian).

ⓘ

Referenced by:: 4th item.
Encodings:: BibTeX

►

H. A. Yamani and L. Fishman (1975)

J

-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering. J. Math. Phys. 16, pp. 410–420.

ⓘ

Referenced by:: §18.39(iv).
Encodings:: BibTeX

… ►

A. J. Yee (2004) Partitions with difference conditions and Alder’s conjecture. Proc. Natl. Acad. Sci. USA 101 (47), pp. 16417–16418.

ⓘ

External Links:: ISSN 1091-6490, FullText, Document, MathReview (Scott D. Ahlgren), ZentralBlatt
Referenced by:: §26.10(iv).
Encodings:: BibTeX

… ►

D. M. Young and R. T. Gregory (1988) A Survey of Numerical Mathematics. Vol. II. Dover Publications Inc., New York.

ⓘ

Notes:: Corrected reprint of the 1973 original, published by Addison-Wesley
External Links:: ISBN 0-486-65692-6, MathReview, ZentralBlatt
Referenced by:: §3.2(iv).
Encodings:: BibTeX

…

D. Zagier (1989) The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.

ⓘ

External Links:: MathReview (J. Browkin), ZentralBlatt
Referenced by:: §25.12(i).
Encodings:: BibTeX

►

D. Zagier (1998) A modified Bernoulli number. Nieuw Arch. Wisk. (4) 16 (1-2), pp. 63–72.

ⓘ

External Links:: ISSN 0028-9825, MathReview (L. Skula), ZentralBlatt
Referenced by:: §24.16(iii).
Encodings:: BibTeX

… ►

A. Zarzo, J. S. Dehesa, and R. J. Yañez (1995) Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach. Ann. Numer. Math. 2 (1-4), pp. 457–472.

ⓘ

External Links:: ISSN 1021-2655, MathReview (B. D. Agrawal), ZentralBlatt
Referenced by:: §13.9(i), §15.13.
Encodings:: BibTeX

►

D. Zeilberger and D. M. Bressoud (1985) A proof of Andrews’

q

-Dyson conjecture. Discrete Math. 54 (2), pp. 201–224.

ⓘ

External Links:: ISSN 0012-365X, Document, MathReview (Ira Gessel), ZentralBlatt
Referenced by:: §17.14.
Encodings:: BibTeX

… ►

S. Zhang and J. Jin (1996) Computation of Special Functions. John Wiley & Sons Inc., New York.

ⓘ

Notes:: Includes diskette containing a large collection of mathematical function software written in Fortran. Implementation in double precision. Maximum accuracy 16S.
External Links:: ISBN 0-471-11963-6, MathReview (Walter Gautschi), ZentralBlatt
Referenced by:: 6th item, 3rd item, 1st item, 11st item, 7th item, 2nd item, 6th item, 3rd item, 2nd item, 5th item, 8th item, 4th item, 2nd item, §19.37(ii), §19.37(iii), §19.37(iii), §22.21, §24.19(i), §28.1, item (b), item (d), 8th item, 3rd item, 6th item, §5.22(ii), §5.22(iii), 2nd item, 2nd item, 4th item, 2nd item, 2nd item, §8.17(v), 4th item, 2nd item, 5th item, 3rd item, 3rd item, 3rd item, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

…

14: Bibliography U

… ►

K. M. Urwin (1965) Integral equations for the paraboloidal wave functions. II. Quart. J. Math. Oxford Ser. (2) 16, pp. 257–262.

ⓘ

External Links:: Document, MathReview (J. Meixner), ZentralBlatt
Referenced by:: §28.31(iii), §28.31(iii).
Encodings:: BibTeX

►

J. V. Uspensky and M. A. Heaslet (1939) Elementary Number Theory. McGraw-Hill Book Company, Inc., New York.

ⓘ

External Links:: MathReview (D. H. Lehmer), ZentralBlatt
Referenced by:: §24.10(iii).
Encodings:: BibTeX

►

T. Uzer, J. T. Muckerman, and M. S. Child (1983) Collisions and umbilic catastrophes. The hyperbolic umbilic canonical diffraction integral. Molecular Phys. 50 (6), pp. 1215–1230.

ⓘ

External Links:: ISSN 0026-8976, Document, MathReview (D. R. J. Chillingworth)
Referenced by:: §36.14(iii).
Encodings:: BibTeX

15: 26.6 Other Lattice Path Numbers

… ►

Delannoy Number $D(m,n)$

►

D(m,n)

is the number of paths from

(0,0)

(m,n)

that are composed of directed line segments of the form

(1,0)

(0,1)

, or

(1,1)

. … ►

Table 26.6.1: Delannoy numbers

D(m,n)

► ►►

$m$	$n$
$m$	…

► … ►

26.6.4

r(n)=D(n,n)-D(n+1,n-1),

n\geq 1

ⓘ

Defines:: $r(n)$ : Schröder number (locally)
Symbols:: $n$ : nonnegative integer and $D(m,n)$ : Delannoy number
Referenced by:: §26.6(i)
Permalink:: http://dlmf.nist.gov/26.6.E4
Encodings:: pMML, png, TeX
See also:: Annotations for §26.6(i), §26.6(i), §26.6 and Ch.26

… ►

26.6.10

D(m,n)=D(m,n-1)+D(m-1,n)+D(m-1,n-1),

m,n\geq 1

ⓘ

Symbols:: $m$ : nonnegative integer, $n$ : nonnegative integer and $D(m,n)$ : Delannoy number
Referenced by:: §26.6(iii)
Permalink:: http://dlmf.nist.gov/26.6.E10
Encodings:: pMML, png, TeX
See also:: Annotations for §26.6(iii), §26.6 and Ch.26

…

16: Bibliography S

… ►

K. Schulten and R. G. Gordon (1975a) Exact recursive evaluation of

3j

- and

6j

-coefficients for quantum-mechanical coupling of angular momenta. J. Mathematical Phys. 16 (10), pp. 1961–1970.

ⓘ

External Links:: Document, MathReview (J.-L. Calais)
Referenced by:: §34.13, §34.3(iii).
Encodings:: BibTeX

… ►

C. Schwartz (1961) Variational calculations of scattering. Ann. Phys. 16, pp. 36–50.

ⓘ

Referenced by:: §18.39(iv).
Encodings:: BibTeX

… ►

B. D. Sleeman (1969) Non-linear integral equations for Heun functions. Proc. Edinburgh Math. Soc. (2) 16, pp. 281–289.

ⓘ

External Links:: Document, MathReview (J. D. DePree), ZentralBlatt
Referenced by:: §31.10(ii).
Encodings:: BibTeX

… ►

D. M. Smith (2011) Algorithm 911: multiple-precision exponential integral and related functions. ACM Trans. Math. Software 37 (4), pp. Art. 46, 16.

ⓘ

External Links:: Document, ZentralBlatt
Referenced by:: 5th item, §4.48(iii), 3rd item, §6.21(ii).
Encodings:: BibTeX

… ►

B. Sommer and J. G. Zabolitzky (1979) On numerical Bessel transformation. Comput. Phys. Comm. 16 (3), pp. 383–387.

ⓘ

Notes:: Single-precision Fortran, maximum accuracy 15D.
External Links:: ISSN 0010-4655, Document, Code
Referenced by:: 8th item.
Encodings:: BibTeX

…

17: 20 Theta Functions

…

18: Adri B. Olde Daalhuis

… ►D. … ►

16 Generalized Hypergeometric Functions & Meijer G-Function

19: Bibliography I

… ►

K. Inkeri (1959) The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

ⓘ

External Links:: MathReview (D. H. Lehmer), ZentralBlatt
Referenced by:: §24.12(i).
Encodings:: BibTeX

… ►

M. E. H. Ismail and D. R. Masson (1994)

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

… ►

M. E. H. Ismail, D. R. Masson, and M. Rahman (Eds.) (1997) Special Functions,

q

-Series and Related Topics. Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.

ⓘ

External Links:: ISBN 0-8218-0524-X, Document, Link, MathReview Entry, ZentralBlatt
Referenced by:: Profile Mourad E.H. Ismail.
Encodings:: BibTeX

… ►

A. R. Its and A. A. Kapaev (2003) Quasi-linear Stokes phenomenon for the second Painlevé transcendent. Nonlinearity 16 (1), pp. 363–386.

ⓘ

External Links:: ISSN 0951-7715, Document, MathReview (Youmin Lu), ZentralBlatt
Referenced by:: §32.12(ii).
Encodings:: BibTeX

… ►

K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida (1991) 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

20: 7.7 Integral Representations

… ►Integrals of the type

\int e^{-z^{2}}R(z)\,\mathrm{d}z

, where

R(z)

is an arbitrary rational function, can be written in closed form in terms of the error functions and elementary functions. ►

7.7.1

\operatorname{erfc}z=\frac{2}{\pi}e^{-z^{2}}\int_{0}^{\infty}\frac{e^{-z^{2}t^% {2}}}{t^{2}+1}\,\mathrm{d}t,

|\operatorname{ph}z|\leq\frac{1}{4}\pi

ⓘ

Symbols:: $\pi$ : the ratio of the circumference of a circle to its diameter, $\operatorname{erfc}\NVar{z}$ : complementary error function, $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $\mathrm{e}$ : base of natural logarithm, $\int$ : integral, $\operatorname{ph}$ : phase and $z$ : complex variable
A&S Ref:: 7.4.11 (in different form)
Referenced by:: §7.11, §7.7(i)
Permalink:: http://dlmf.nist.gov/7.7.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §7.7(i), §7.7 and Ch.7

►

7.7.2

w\left(z\right)=\frac{1}{\pi i}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\,% \mathrm{d}t}{t-z}=\frac{2z}{\pi i}\int_{0}^{\infty}\frac{e^{-t^{2}}\,\mathrm{d% }t}{t^{2}-z^{2}},

\Im z>0

ⓘ

Symbols:: $\pi$ : the ratio of the circumference of a circle to its diameter, $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $w\left(\NVar{z}\right)$ : Faddeeva (or Faddeyeva) function, $\mathrm{e}$ : base of natural logarithm, $\Im$ : imaginary part, $\mathrm{i}$ : imaginary unit, $\int$ : integral and $z$ : complex variable
A&S Ref:: 7.1.4 (in different form)
Referenced by:: §7.19(i), §7.22(i), §7.7(i)
Permalink:: http://dlmf.nist.gov/7.7.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §7.7(i), §7.7 and Ch.7

… ►

7.7.9

\int_{0}^{x}\operatorname{erf}t\,\mathrm{d}t=x\operatorname{erf}x+\frac{1}{% \sqrt{\pi}}\left(e^{-x^{2}}-1\right).

ⓘ

Symbols:: $\pi$ : the ratio of the circumference of a circle to its diameter, $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $\operatorname{erf}\NVar{z}$ : error function, $\mathrm{e}$ : base of natural logarithm, $\int$ : integral and $x$ : real variable
A&S Ref:: 7.4.35 (in different form)
Referenced by:: §7.7(i)
Permalink:: http://dlmf.nist.gov/7.7.E9
Encodings:: pMML, png, TeX
See also:: Annotations for §7.7(i), §7.7 and Ch.7

… ►In (7.7.13) and (7.7.14) the integration paths are straight lines,

\zeta=\frac{1}{16}\pi^{2}z^{4}

, and

c

is a constant such that

0<c<\frac{1}{4}

in (7.7.13), and

0<c<\frac{3}{4}

in (7.7.14). …

大学结业证书是什么学历〖办证V信ATV1819〗16d

11—20 of 501 matching pages

11: 27.15 Chinese Remainder Theorem

12: Bibliography Y

13: Bibliography Z

14: Bibliography U

15: 26.6 Other Lattice Path Numbers

Delannoy Number D ⁡ ( m , n )

16: Bibliography S

17: 20 Theta Functions

18: Adri B. Olde Daalhuis

19: Bibliography I

20: 7.7 Integral Representations

Delannoy Number $D(m,n)$