common

SearchAdvancedHelp

(0.001 seconds)

21—30 of 36 matching pages

21: 22.20 Methods of Computation

… ►Then as $n\to \mathrm{\infty }$ sequences $\{a_n\}$, $\{b_n\}$ converge to a common limit $M=M(a_0,b_0)$, the arithmetic-geometric mean of $a_0,b_0$. …

22: 26.10 Integer Partitions: Other Restrictions

… ►

26.10.18

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $\left(m,n\right)$: greatest common divisor (gcd), $\mathrm{i}$: imaginary unit, $h$: nonnegative integer, $k$: nonnegative integer, $n$: nonnegative integer, $A_k(n)$: coefficient and $f(h,k)$: function

Permalink:

http://dlmf.nist.gov/26.10.E18

Encodings:

pMML, png, TeX

See also:

Annotations for §26.10(vi), §26.10 and Ch.26

…

23: 36.5 Stokes Sets

…

24: 24.4 Basic Properties

… ►

24.4.11 $$\sum _{\begin{array}{c}k=1\\ \left(k,m\right)=1\end{array}}^m{k}^n=\frac{1}{n+1}\sum _{j=1}^{n+1}\left(\genfrac{}{}{0pt}{}{n+1}{j}\right)\left(\prod _{p|m}(1-p^{n-j})B_{n+1-j}\right)m^j.$$

ⓘ

Symbols:

$B_n$: Bernoulli numbers, $\left(\genfrac{}{}{0.0pt}{}{m}{n}\right)$: binomial coefficient, $\left(m,n\right)$: greatest common divisor (gcd), $j$: integer, $k$: integer, $m$: integer, $n$: integer and $p$: prime

Referenced by:

§24.4(iii)

Permalink:

http://dlmf.nist.gov/24.4.E11

Encodings:

pMML, png, TeX

See also:

Annotations for §24.4(iii), §24.4 and Ch.24

…

25: 13.20 Uniform Asymptotic Approximations for Large $\mu$

… ►It should be noted that (13.20.11), (13.20.16), and (13.20.18) differ only in the common error terms. …

26: 19.8 Quadratic Transformations

… ►As $n\to \mathrm{\infty }$, $a_n$ and $g_n$ converge to a common limit $M(a_0,g_0)$ called the AGM (Arithmetic-Geometric Mean) of $a_0$ and $g_0$. …

27: 19.36 Methods of Computation

… ►The incomplete integrals $R_F(x,y,z)$ and $R_G(x,y,z)$ can be computed by successive transformations in which two of the three variables converge quadratically to a common value and the integrals reduce to $R_C$, accompanied by two quadratically convergent series in the case of $R_G$; compare Carlson (1965, §§5,6). …

28: 2.5 Mellin Transform Methods

… ►If $ℳf\left(1-z\right)$ and $ℳh\left(z\right)$ have a common strip of analyticity , then … ►To apply the Mellin transform method outlined in §2.5(i), we require the transforms $ℳf\left(1-z\right)$ and $ℳh\left(z\right)$ to have a common strip of analyticity. …

29: 18.39 Applications in the Physical Sciences

… ►The nature of, and notations and common vocabulary for, the eigenvalues and eigenfunctions of self-adjoint second order differential operators is overviewed in §1.18. … ►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry. …

30: Bibliography B

… ►

The SLATEC Common Mathematical Library. In Sources and Development of Mathematical Software, W. R. Cowell (Ed.), pp. 302–320.

ⓘ

External Links:

GAMS (package SLATEC)

Referenced by:

SLATEC (free Fortran library).

Encodings:

BibTeX

…