hypergeometric2f1(a, b, c, z)
Overview
The hypergeometric2f1 function calculates the hypergeometric function \, _2F_1(a, b; c; z) using a series approximation.
Parameters
| Parameter | Type | Description |
|---|---|---|
a |
Number | First parameter of the hypergeometric function. |
b |
Number | Second parameter of the hypergeometric function. |
c |
Number | Third parameter of the hypergeometric function. |
z |
Number | Argument for which the hypergeometric function is calculated. |
Returns
| Return | Type | Description |
|---|---|---|
hypergeom |
Number | The calculated hypergeometric function value. |
Example
local a = 1
local b = 2
local c = 3
local z = 0.5
local result = StatBook.hypergeometric2f1(a, b, c, z)
print(result) -- Output will vary depending on input parameters
Mathematical Background
The hypergeometric function \, _2F_1(a, b; c; z) is computed using the following series approximation:
\, _2F_1(a, b; c; z) = 1 + \frac{a \cdot b}{c \cdot 1!} \cdot z + \frac{a(a+1) \cdot b(b+1)}{c(c+1) \cdot 2!} \cdot z^2 + \ldots
The calculation continues until the change between the new sum and the previous sum is less than a tolerance value of 1 \times 10^{-6} or up to 100,000,000 iterations.