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 hypergeometric function?
A generalized hypergeometric function is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ratio of successive terms can be written. (1) (The factor of. in the denominator is present for historical reasons of notation.)
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. Who discovered 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).
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 calculate hypergeometric probability?
The probability of getting EXACTLY 3 red cards would be an example of a hypergeometric probability, which is indicated by the following notation: P(X = 3). The probability of getting exactly 3 red cards is 0.325. Thus, P(X = 3) = 0.325.
Frequently Asked Questions(FAQ)
Why is it called hypergeometric distribution?
Because these go over or beyond the geometric progression (for which the rational function is constant), they were termed hypergeometric from the ancient Greek prefix ˊυ′περ (hyper).
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)
Where is hypergeometric distribution used?
When do we use the hypergeometric distribution? The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.
How do you know if it is a hypergeometric distribution?
The hypergeometric distribution is defined by 3 parameters: population size, event count in population, and sample size. For example, you receive one special order shipment of 500 labels. Suppose that 2% of the labels are defective. The event count in the population is 10 (0.02 * 500).
What is hypergeometric distribution in statistics?
What is capital gamma in math?
In mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
What is Legendre differential equation?
Since the Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind.
How many singular points does a hypergeometric equation have?
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 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.
Why hypergeometric distribution is important?
The hypergeometric test is used to determine the statistical significance of having drawn k k k objects with a desired property from a population of size N N N with K K K total objects that have the desired property.
What is interpretation of N in hypergeometric distribution?
If the variable N describes the number of all marbles in the urn (see contingency table below) and K describes the number of green marbles, then N − K corresponds to the number of red marbles. In this example, X is the random variable whose outcome is k, the number of green marbles actually drawn in the experiment.
Is hypergeometric distribution continuous?
For the hypergeometric to work, the population must be dividable into two and only two independent subsets (aces and non-aces in our example). The random variable X = the number of items from the group of interest. … the random variable must be discrete, rather than continuous.
What is an example of hypergeometric distribution?
Hypergeometric Distribution Example 1 A deck of cards contains 20 cards: 6 red cards and 14 black cards. 5 cards are drawn randomly without replacement. … 6C4 means that out of 6 possible red cards, we are choosing 4. 14C1 means that out of a possible 14 black cards, we’re choosing 1.
When can binomial approximate hypergeometric?
As a rule of thumb, if the population size is more than 20 times the sample size (N > 20 n), then we may use binomial probabilities in place of hypergeometric probabilities. We next illustrate this approximation in some examples.
Which of the following are the assumptions for the hypergeometric test?
The following assumptions and rules apply to use the Hypergeometric Distribution: Discrete distribution. Population, N, is finite and a known value. Two outcomes – call them SUCCESS (S) and FAILURE (F).
Who first discovered the binomial distribution?
Bernoulli The binomial distribution is one of the oldest known probability distributions. It was discovered by Bernoulli, J. in his work entitled Ars Conjectandi (1713).
What is Gamma in Matlab?
The gamma function is defined for real x > 0 by the integral: Γ ( x ) = ∫ 0 ∞ e − t t x − 1 d t. The gamma function interpolates the factorial function.
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