Reference · Math

math.gamma

math.gamma(num) -> float

What it does

The gamma function, as Python's math.gamma: the factorial extended to any number, as a float, with math.gamma(n) equal to (n - 1)! for a positive int n. math.gamma(5) is 24.0, math.gamma(0.5) is the square root of pi. It reaches past where math.factorial overflows an int, up to math.gamma(171), which is 170!.

Examples

print(math.gamma(5), math.gamma(1), math.gamma(6) == math.factorial(5))print(math.gamma(0.5), math.gamma(1.5), math.gamma(10.5))

24.0 1.0 true1.772453850905516 0.886226925452758 1133278.3889487854

Edge cases

• Negative non-integers have a value: math.gamma(-0.5) is about -3.545, and math.gamma(-1.5) is positive again.
• The answer is a float with a float's precision: math.gamma(0.5) * math.gamma(0.5) is pi to the last digit or so, not exactly.
• Values near zero grow without bound: math.gamma(1e-300) is about 1e300.
• Plus infinity gives infinity, not an error; NaN stays NaN.

print(math.gamma(-0.5), math.gamma(-1.5), math.gamma(171) > 1e306)print(math.isclose(math.gamma(0.5) * math.gamma(0.5), math.pi))print(math.gamma(float("inf")), math.gamma(float("nan")))

-3.5449077018110318 2.363271801207355 truetrueinf NaN

Errors

Zero and the negative ints are the poles: math.gamma(0) and math.gamma(-2) are a runtime error, math domain error, not an error value and not infinity, as Python's ValueError. So is minus infinity. A result too large for a float, math.gamma(172) and up, is a runtime error, math range error; take math.lgamma instead. An argument that is not a number is a runtime error as well.

print(math.gamma(0))

line 1: `math.gamma`: math domain error (0)

print(math.gamma(-2))

line 1: `math.gamma`: math domain error (-2)

print(math.gamma(172))

line 1: `math.gamma`: math range error (172)

Chaining

In a pipeline the number comes first:

print(5 | math.gamma)print([1, 2, 3, 4, 5] | map(math.gamma))

24.0[1.0, 1.0, 2.0, 6.0, 24.0]

See also

math.lgamma, math.factorial, math.erf, math.exp

Edit this page on GitHub · every example's output was made by running it (tools/refcheck.mjs) · questions on Discord or r/quillo