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RedHat 9 (Linux i386) - man page for combinatorics (redhat section n)

combinatorics(n)			 Tcl Math Library			 combinatorics(n)

       combinatorics - Combinatorial functions in the Tcl Math Library

       package require Tcl 8.2

       package require math ?1.2?

       ::math::ln_Gamma z

       ::math::factorial x

       ::math::choose n k

       ::math::Beta z w

       The  math  package  contains  implementations of several functions useful in combinatorial

       ::math::ln_Gamma z
	      Returns the natural logarithm of the Gamma function for the argument z.

	      The Gamma function is defined as the improper integral from zero to positive infin-
	      ity of
		t**(x-1)*exp(-t) dt

	      The  approximation used in the Tcl Math Library is from Lanczos, ISIAM J. Numerical
	      Analysis, series B, volume 1, p. 86.  For "x > 1", the absolute error of the result
	      is  claimed to be smaller than 5.5*10**-10 -- that is, the resulting value of Gamma
		exp( ln_Gamma( x) )
	      is computed is expected to be precise to better than nine significant figures.

       ::math::factorial x
	      Returns the factorial of the argument x.

	      For integer x, 0 <= x <= 12, an exact integer result is returned.

	      For integer x, 13 <= x <=  21,  an  exact  floating-point  result  is  returned  on
	      machines with IEEE floating point.

	      For integer x, 22 <= x <= 170, the result is exact to 1 ULP.

	      For  real  x,  x >= 0, the result is approximated by computing Gamma(x+1) using the
	      ::math::ln_Gamma function, and the result is expected to be precise to better  than
	      nine significant figures.

	      It is an error to present x <= -1 or x > 170, or a value of x that is not numeric.

       ::math::choose n k
	      Returns the binomial coefficient C(n, k)
		 C(n,k) = n! / k! (n-k)!
	      If  both	parameters  are  integers  and	the result fits in 32 bits, the result is
	      rounded to an integer.

	      Integer results are exact up to at least n = 34.	Floating point results	are  pre-
	      cise to better than nine significant figures.

       ::math::Beta z w
	      Returns the Beta function of the parameters z and w.
		 Beta(z,w) = Beta(w,z) = Gamma(z) * Gamma(w) / Gamma(z+w)
	      Results are returned as a floating point number precise to better than nine signif-
	      icant digits provided that w and z are both at least 1.

math					       4.2				 combinatorics(n)

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