What do you mean by confluent hypergeometric function?

In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity.

What is Hypergeom in Matlab?

Hypergeometric Function for Numeric and Symbolic Arguments Return exact symbolic results by converting at least one of the inputs to symbolic form by using sym . For most symbolic (exact) inputs, hypergeom returns unresolved symbolic calls.

Why hypergeometric function is called hypergeometric?

We have seen that the hypergeometric series in (4) converges absolutely, when and, thus, defines a function: 2 F 1 ( a , b ; c ; z ) , which is analytic, when provided that c is neither zero nor a negative integer. This function is correspondingly called the hypergeometric function or Gauss’s hypergeometric function.

How do you calculate hypergeometric distribution?

Hypergeometric Formula.. The hypergeometric distribution has the following properties: The mean of the distribution is equal to n * k / N . The variance is n * k * ( N – k ) * ( N – n ) / [ N2 * ( N – 1 ) ] .

How many singular points does a hypergeometric equation have?

three regular singular points
The hypergeometric differential equation. which has three regular singular points: 0,1 and ∞.

What is the hypergeometric function used for?

Hypergeometric functions show up as solutions of many important ordinary differential equations. In particular in physics, for example in the study of the hydrogene atom (Laguerre polynomials) and in simple problems of classical mechanics (Hermite polynomials appear in the study of the harmonic oscillator).

Who invented hypergeometric series?

The term “hypergeometric series” was first used by John Wallis in his 1655 book Arithmetica Infinitorum. Hypergeometric series were studied by Leonhard Euler, but the first full systematic treatment was given by Carl Friedrich Gauss (1813).

What is the property of a hypergeometric distribution?

The hypergeometric distribution has the following properties: The mean of the distribution is equal to n * k / N . The variance is n * k * ( N – k ) * ( N – n ) / [ N2 * ( N – 1 ) ] .

What are hypergeometric series used for?