Reciprocal Gamma Function 1/Γ(x) Calculator

Enter a real number x to compute the reciprocal gamma function 1/Γ(x). It is an entire function defined for all real x, equal to exactly 0 at zero and the negative integers. Shows Γ(x) for reference plus a curve.

Input

Enter a real number x to compute the reciprocal gamma function 1/Γ(x). At zero and the negative integers the value is exactly 0.

Argument x

Enter any real number (e.g. 4.5, -2.5, 0)

Result

Value of 1/Γ(4.5)

0.0859717461

1/Γ(x) is the reciprocal of the gamma function, an entire function defined for all real x.

Γ(x) (reference)

11.6317283966

Domain

All real numbers

Graph of 1/Γ(x)

Curve over the range -4 to 5. The orange dot marks the position of your input x.

How it works

1/Γ(x) is an entire function defined for all real x (indeed the whole complex plane) and has no poles.
At the non-positive integers x = 0, -1, -2, … the value 1/Γ(x) = 0, matching the poles of Γ(x) there.
For the positive region it computes 1/Γ(x) = 1 / Γ(x), with Γ(x) evaluated by the Lanczos approximation.
For x below 0.5 it uses the reflection formula 1/Γ(x) = sin(πx)/π · Γ(1-x).
Inputs with very large absolute value are restricted to avoid precision loss and overflow.

Reviews

Tell us what you think of this calculator.