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/dports/math/p5-Math-Prime-Util/Math-Prime-Util-0.73/t/
H A D27-bernfrac.t75 my @stirling1 = (
100 $#stirling1 = 12;
108 + 2 + scalar(@stirling3) + scalar(@stirling2) + scalar(@stirling1) + 2*$extra
175 foreach my $narr (@stirling1) {
/dports/math/reduce/Reduce-svn5758-src/packages/specfn/
H A Dsfbinom.red69 algebraic operator stirling1, stirling2;
72 let {stirling1(~n,~n) => 1,
73 stirling1(~n,0) => 0 when not(n=0),
74 stirling1(~n,~n-1) => - binomial(n,2),
75 stirling1(~n,~m) => 0 when fixp n and fixp m and n < m,
76 stirling1(~n,~m) => (for k:=0:(n-m) sum
98 put('stirling1, 'prifn, 'plain!-symbol);
100 put('stirling1, 'plain!-functionsymbol, '!s);
102 % put('stirling1, 'fancy!-functionsymbol, "\mathrm{s}");
/dports/math/p5-Math-Prime-Util-GMP/Math-Prime-Util-GMP-0.52/t/
H A D24-bernfrac.t59 my @stirling1 = (
83 plan tests => 2 + scalar(@stirling3) + scalar(@stirling2) + scalar(@stirling1) + 3 + 2+6 + 4;
110 foreach my $narr (@stirling1) {
/dports/math/maxima/maxima-5.43.2/tests/
H A Drtestnset.mac1123 stirling1(b,a);
1124 stirling1(b,a)$
1188 stirling1(n,n);
1191 stirling1(kk,kk);
1194 stirling1(1,kk);
1195 stirling1(1,kk)$
1197 stirling1(1,k);
1200 stirling1(n,0);
1201 stirling1(n,0)$
1206 stirling1(n,1);
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/dports/math/maxima/maxima-5.43.2/tests/wester_problems/
H A Dtest_combinatorics.mac38 /*stirling1(5, 2);*/
/dports/math/fricas/fricas-1.3.7/src/algebra/
H A Dcombinat.spad44 stirling1 : (I, I) -> I
45 ++ \spad{stirling1(n, m)} returns the Stirling number of the first kind
157 stirling1(n, m) ==
/dports/math/pari/pari-2.13.3/src/functions/combinatorics/
H A Dstirling40 Variant: Also available are \fun{GEN}{stirling1}{ulong n, ulong k}
/dports/math/py-mpmath/mpmath-1.2.1/mpmath/libmp/
H A D__init__.py73 list_primes, isprime, moebius, gcd, eulernum, stirling1, stirling2)
H A Dlibintmath.py549 def stirling1(n, k): function
/dports/math/calc/calc-2.14.0.14/cal/
H A Dfactorial2.cal486 define stirling1(n,m){
488 if(n<0)return newerror("stirling1(n,m): n <= 0");
489 if(m<0)return newerror("stirling1(n,m): m < 0");
712 print "stirling1(n,m)";
H A Dtest8900.cal2008 if ((stirling1(10, 0) - (0)) != 0) {
2012 if ((stirling1(0, 10) - (0)) != 0) {
2016 if ((stirling1(0, 0) - (1)) != 0) {
2020 if ((stirling1(10, 10) - (1)) != 0) {
2024 if ((stirling1(10, 1) - (-362880)) != 0) {
2028 if ((stirling1(10, 5) - (-269325)) != 0) {
/dports/math/py-mpmath/mpmath-1.2.1/mpmath/
H A Dfunction_docs.py9967 stirling1 = r""" variable
H A D__init__.py426 stirling1 = mp.stirling1 variable
H A Dctx_base.py350 _stirling1 = staticmethod(libmp.stirling1)
/dports/math/maxima/maxima-5.43.2/doc/info/
H A Dnset.texi2010 @anchor{stirling1}
2011 @deffn {Function} stirling1 (@var{n}, @var{m})
2016 integers, the magnitude of @code{stirling1 (@var{n}, @var{m})} is the number of
2019 @code{stirling1} is a simplifying function.
2024 @math{stirling1(1,k) = kron_delta(1,k), k >= 0},(see @url{http://dlmf.nist.gov/26.8.E2})
2026 @math{stirling1(n,n) = 1, n >= 0} (see @url{http://dlmf.nist.gov/26.8.E1})
2033 @math{stirling1(n,1) =(-1)^(n-1) (n-1)!, n >= 1} (see @url{http://dlmf.nist.gov/26.8.E14})
2035 @math{stirling1(n,k) = 0, n >= 0} and @math{k > n}.
2040 @code{stirling1} does not simplify for non-integer arguments.
2048 @c stirling1 (n, n);
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/dports/math/p5-Math-Prime-Util/Math-Prime-Util-0.73/
H A Dutil.h79 extern IV stirling1(UV n, UV m);
/dports/math/maxima/maxima-5.43.2/doc/info/pt.utf8/
H A Dmaxima.info192 Ref: stirling11068650
H A Dmaxima.info-43428 -- Função da class: stirling1 (<n>, <m>)
3443 1. stirling1(0, n) = kron_delta(0, n) (Ref. [1])
3444 2. stirling1(n, n) = 1 (Ref. [1])
3446 4. stirling1(n + 1, 0) = 0 (Ref. [1])
3447 5. stirling1(n + 1, 1) = n! (Ref. [1])
3448 6. stirling1(n + 1, 2) = 2^n - 1 (Ref. [1])
3464 (%i3) stirling1 (n, n);
3469 (%i1) stirling1 (sqrt(2), sqrt(2));
3472 Maxima aplica identidades a 'stirling1'.
3476 (%i3) stirling1 (n + 1, n);
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/dports/math/maxima/maxima-5.43.2/doc/info/pt/
H A Dmaxima.info192 Ref: stirling11068652
/dports/math/py-mpmath/mpmath-1.2.1/mpmath/functions/
H A Dfunctions.py632 def stirling1(ctx, n, k, exact=False): function
/dports/math/maxima/maxima-5.43.2/doc/info/de.utf8/
H A Dmaxima.info-31689 -- Funktion: stirling1 (<n>, <m>)
1704 * 'stirling1(0, n) = kron_delta(0, n)'
1705 * 'stirling1(n, n) = 1'
1706 * 'stirling1(n, n - 1) = binomial(n, 2)'
1707 * 'stirling1(n + 1, 0) = 0'
1708 * 'stirling1(n + 1, 1) = n!'
1709 * 'stirling1(n + 1, 2) = 2^n - 1'
1725 (%i3) stirling1 (n, n);
1731 (%i1) stirling1 (sqrt(2), sqrt(2));
1738 (%i3) stirling1 (n + 1, n);
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/dports/math/maxima/maxima-5.43.2/doc/info/de/
H A Dmaxima.info-31689 -- Funktion: stirling1 (<n>, <m>)
1704 * 'stirling1(0, n) = kron_delta(0, n)'
1705 * 'stirling1(n, n) = 1'
1706 * 'stirling1(n, n - 1) = binomial(n, 2)'
1707 * 'stirling1(n + 1, 0) = 0'
1708 * 'stirling1(n + 1, 1) = n!'
1709 * 'stirling1(n + 1, 2) = 2^n - 1'
1725 (%i3) stirling1 (n, n);
1731 (%i1) stirling1 (sqrt(2), sqrt(2));
1738 (%i3) stirling1 (n + 1, n);
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/dports/math/maxima/maxima-5.43.2/doc/info/es/
H A Dmaxima.info-51387 -- Funci�n: stirling1 (<n>, <m>)
1402 1. stirling1(0, n) = kron_delta(0, n) (Ref. [1])
1403 2. stirling1(n, n) = 1 (Ref. [1])
1405 4. stirling1(n + 1, 0) = 0 (Ref. [1])
1406 5. stirling1(n + 1, 1) = n! (Ref. [1])
1407 6. stirling1(n + 1, 2) = 2^n - 1 (Ref. [1])
1423 (%i3) stirling1 (n, n);
1429 (%i1) stirling1 (sqrt(2), sqrt(2));
1432 Maxima aplicas algunas identidades a 'stirling1',
1436 (%i3) stirling1 (n + 1, n);
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/dports/math/maxima/maxima-5.43.2/doc/info/es.utf8/
H A Dmaxima.info-51387 -- Función: stirling1 (<n>, <m>)
1402 1. stirling1(0, n) = kron_delta(0, n) (Ref. [1])
1403 2. stirling1(n, n) = 1 (Ref. [1])
1405 4. stirling1(n + 1, 0) = 0 (Ref. [1])
1406 5. stirling1(n + 1, 1) = n! (Ref. [1])
1407 6. stirling1(n + 1, 2) = 2^n - 1 (Ref. [1])
1423 (%i3) stirling1 (n, n);
1429 (%i1) stirling1 (sqrt(2), sqrt(2));
1432 Maxima aplicas algunas identidades a 'stirling1',
1436 (%i3) stirling1 (n + 1, n);
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/dports/math/maxima/maxima-5.43.2/doc/info/pt_BR/
H A Dmaxima.info-43486 -- Fun��o: stirling1 (<n>, <m>)
3501 1. stirling1(0, n) = kron_delta(0, n) (Ref. [1])
3502 2. stirling1(n, n) = 1 (Ref. [1])
3504 4. stirling1(n + 1, 0) = 0 (Ref. [1])
3505 5. stirling1(n + 1, 1) = n! (Ref. [1])
3506 6. stirling1(n + 1, 2) = 2^n - 1 (Ref. [1])
3522 (%i3) stirling1 (n, n);
3527 (%i1) stirling1 (sqrt(2), sqrt(2));
3530 Maxima aplica identidades a 'stirling1'.
3534 (%i3) stirling1 (n + 1, n);
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