Returns a generalization of Pochhammer's symbol.
double
value specifying the first argument. double
value specifying the second, differential argument. A double
value specifying the generalized Pochhammer symbol, Gamma(a+x)/Gamma(a).
Method Poch
evaluates Pochhammer's symbol for n a nonnegative integer. Pochhammer's generalized symbol is defined to be
See Gamma
for the definition of .
Note that a straightforward evaluation of Pochhammer's generalized symbol with either Gamma or Log Gamma functions can be especially unreliable when a is large or x is small.
Substantial loss can occur if a + x or a are close to a negative integer unless is sufficiently small. To insure that the result does not overflow or underflow, one can keep the arguments a and a + x well within the range dictated by the Gamma function method Gamma or one can keep small whenever a is large. Poch
also works for a variety of arguments outside these rough limits, but any more general limits that are also useful are difficult to specify.
Sfun Class | Imsl.Math Namespace | Example