How do you write a 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 are hypergeometric series 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).
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.
How do you solve hypergeometric series?
This a hypergeometric equation with constants a, b and c defined by F = c, G = -(a + b + 1) and H = -ab and can therefore be solved near t = 0 and t = 1 in terms of the hypergeometric function. But this means that (0.8) can be solved in terms of the same function near x = A and x = B.
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 many singular points of hypergeometric equation?
three regular singular points
The hypergeometric equation is a differential equation with three regular singular points (cf. Regular singular point) at 0, 1 and ∞ such that both at 0 and 1 one of the exponents equals 0.
What does Hypergeom mean 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.
How do you do hypergeometric distribution in Excel?
HYPGEOM. DIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size. Use HYPGEOM….Example.
| Data | Description | Result |
|---|---|---|
| =HYPGEOM.DIST(A2,A3,A4,A5,FALSE) | Probability hypergeometric distribution function, for sample and in cells A2 through A5. | 0.3633 |
Who discovered hypergeometric distribution?
The term HYPERGEOMETRIC (to describe a particular differential equation) is due to Johann Friedrich Pfaff (1765-1825) (Kline, page 489).
How do you write a hypergeometric function in Matlab?
Hypergeometric Function for Numeric and Symbolic Arguments
- A = [hypergeom([1 2], 2.5, 2),…
- A = -1.2174 – 0.8330i 1.2091 + 0.0000i -0.2028 + 0.2405i.
- symA = [hypergeom([1 2], 2.5, sym(2)),…
- symA = [ hypergeom([1, 2], 5/2, 2), hypergeom(1/3, [2, 3], pi), hypergeom([1/2, 1], 1/3, 3i)]
- vpa(symA)
What is functional notation?
Functional notation is a way of representing functions algebraically. Function notation makes it easier to recognize the independent and dependent variables in an equation. The functionf( x) is read as “f of x” and indicates that x is the independent variable.
How to show inputs in function notation?
However, with the function notation, you could use g (x) or h (x) to indicate other functions of x. With the notation that uses y, you cannot see the inputs.
What is wrong with the notation y = 3x + 1?
There is nothing wrong with the notation y = 3x + 1. However, it has some limitations. If you are dealing with more than 1 function, you still have to use y. However, with the function notation, you could use g (x) or h (x) to indicate other functions of x. With the notation that uses y, you cannot see the inputs.
What does f (x) mean in function notation?
The entire symbol, usually f (x), stands for the range set. The ordered-pair numbers become (x, f (x)). The following diagram shows what is function notation.