What do you mean by confluent hyper hypergeometric function?

What do you mean by confluent hyper 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 are hypergeometric functions 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).

How do you find the hypergeometric function?

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 ) ] .

What does Hypergeom mean in Matlab?

Hypergeometric Function for Numeric and Symbolic Arguments Depending on whether the input is floating point or symbolic, hypergeom returns floating point or symbolic results. For most symbolic (exact) inputs, hypergeom returns unresolved symbolic calls.

What is a hypergeometric probability distribution?

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with …

Is the hypergeometric function?

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE).

What is hypergeometric distribution in statistics?

hypergeometric distribution, in statistics, distribution function in which selections are made from two groups without replacing members of the groups. Thus, it often is employed in random sampling for statistical quality control.

How do you use a hypergeometric calculator?

To use it, we need to plug four numbers into the calculator:

1. Population size. In a Magic context, this is the number of cards in the deck when the card draw experiment starts.
2. Number of successes in population.
3. Sample size.
4. Number of successes in sample.

What are the numbers of parameter of hypergeometric distribution?

The hypergeometric distribution is defined by 3 parameters: population size, event count in population, and sample size.

How many parameters are there in hypergeometric distribution?

three parameters
The hypergeometric distribution has three parameters that have direct physical interpretations.

What is a gamma function used for?

While the gamma function behaves like a factorial for natural numbers (a discrete set), its extension to the positive real numbers (a continuous set) makes it useful for modeling situations involving continuous change, with important applications to calculus, differential equations, complex analysis, and statistics.

Which is an example of a confluent hypergeometric function?

For example, if b = 0 and a ≠ 0 then Γ (a+1)U(a, b, z) − 1 is asymptotic to az ln z as z goes to zero. But see #Special cases for some examples where it is an entire function (polynomial).

Which is a special case of the hypergeometric series?

In mathematics, the Gaussian or ordinary hypergeometric function 2F1 ( a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE).

How to find the solution to the hypergeometric function?

Applying Kummer’s 24=6×4 transformations to the hypergeometric function gives the 6 = 2×3 solutions above corresponding to each of the 2 possible exponents at each of the 3 singular points, each of which appears 4 times because of the identities by making the substitution w = uv and eliminating the first-derivative term. One finds that