EQUAL SciMax Toolbox EXCLAM EXCLAM

SciMax Toolbox >> EXCLAM

EXCLAM

Maxima Operator

Calling Sequence

!

Description

The factorial operator. For any complex number x (including integer, rational, and real numbers) except for negative integers, x! is defined as gamma(x+1).

For an integer x, x! simplifies to the product of the integers from 1 to x inclusive. 0! simplifies to 1. For a floating point number x, x! simplifies to the value of gamma (x+1). For x equal to n/2 where n is an odd integer, x! simplifies to a rational factor times sqrt (%pi) (since gamma (1/2) is equal to sqrt (%pi)). If x is anything else, x! is not simplified.

The variables factlim, minfactorial, and factcomb control the simplification of expressions containing factorials.

The functions gamma, bffac, and cbffac are varieties of the gamma function. makegamma substitutes gamma for factorials and related functions.

See also .

The factorial of an integer, half-integer, or floating point argument is simplified unless the operand is greater than factlim.

(%i1) factlim : 10;
(%o1)                          10
(%i2) [0!, (7/2)!, 4.77!, 8!, 20!];
            105 sqrt(%pi)
(%o2)   [1, -------------, 81.44668037931199, 40320, 20!]
                 16

The factorial of a complex number, known constant, or general expression is not simplified. Even so it may be possible simplify the factorial after evaluating the operand.

(%i1) [(%i + 1)!, %pi!, %e!, (cos(1) + sin(1))!];
(%o1)      [(%i + 1)!, %pi!, %e!, (sin(1) + cos(1))!]
(%i2) ev (%, numer, %enumer);
(%o2) [(%i + 1)!, 7.188082728976037, 4.260820476357,
                                               1.227580202486819]

The factorial of an unbound symbol is not simplified.

(%i1) kill (foo);
(%o1)                         done
(%i2) foo!;
(%o2)                         foo!

Factorials are simplified, not evaluated. Thus x! may be replaced even in a quoted expression.

(%i1) '([0!, (7/2)!, 4.77!, 8!, 20!]);
          105 sqrt(%pi)
(%o1) [1, -------------, 81.44668037931199, 40320,
               16
                                             2432902008176640000]
EQUAL SciMax Toolbox EXCLAM EXCLAM