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regularizedBeta -- regularized beta function

Usage:

regularizedBeta(x, a, b)
Inputs:
- x, a real number,
- a, a real number,
- b, a real number,
Outputs:
- a real number,

Description

This is the regularized (incomplete) beta function \(I_x(a, b) = \frac{1}{B(a, b)}\int_0^x t^{a - 1} (1 - t)^{b - 1}\,dt\).

i1 : regularizedBeta(1/2, 3, 4)

o1 = .6562499999999997

o1 : RR (of precision 53)

i2 : 1/Beta(3,4) * integrate(t -> t^2 * (1 - t)^3, 0, 1/2)

o2 = .65625

o2 : RR (of precision 53)

See also

Beta -- Beta function
inverseRegularizedBeta -- inverse of the regularized beta function

Ways to use regularizedBeta:

regularizedBeta(CC,CC,CC)
regularizedBeta(CC,CC,RR)
regularizedBeta(CC,RR,CC)
regularizedBeta(CC,RR,RR)
regularizedBeta(RR,CC,CC)
regularizedBeta(RR,CC,RR)
regularizedBeta(RR,RR,CC)
regularizedBeta(RR,RR,RR)
regularizedBeta(RR,RR,RRi)
regularizedBeta(RR,RRi,RR)
regularizedBeta(RR,RRi,RRi)
regularizedBeta(RRi,RR,RR)
regularizedBeta(RRi,RR,RRi)
regularizedBeta(RRi,RRi,RR)
regularizedBeta(RRi,RRi,RRi)

For the programmer

The object regularizedBeta is a method function.

The source of this document is in Macaulay2Doc/functions/Beta-doc.m2:70:0.