Hypergeometric Definition and 66 Threads

Hey, I want to compute integrals of the following form I= \int_{-i \infty}^{i\infty} (1-x^2)^\frac{d-1}{2} \prod_{i=1}^4 _2F_1(a_i,b_i,c_i;\frac{1-x}{2}) dx where a_i,b_i,c_i are constants and c_i\in \mathbb{N}. d is a positive integer. For odd d I know that the integral will be zero by...

Hello, I am wondering about integrals of the form \int_0^1 {}_p F_q(\{a_1,\ldots,a_p\},\{b_1,\ldots,b_q\},y){}_{p'} F_{q'}(\{a'_1,\ldots,a'_{p'}\},\{b'_1,\ldots,b'_{q'}\},y)dy integrals of product of hypergeometric functions. I know that if the limits of integration were +/-...

Homework Statement Suppose 9 mice are available for a study of a possible carcinogen and 4 of them will form a control group (i.e. will not receive the substance). Assuming that a random sample of 4 mice are selected, what is the probability that a particular mouse, Mike Mouse will be included...

Today, I use two softwares to calculate the value of a hypergeometric functions (2F1). One is Mathematica and another is Matlab. But they give me different results. For examples: (1) 2F1(0.5, 1., 1.5, 5) (Pay an attention to the sign of the image part.) Mathematica's result...

Homework Statement I have seen some hypergeometric function in the form: 2F1=(a,b;c;d), Is there such thing as: 2F1=(a,b,c;d) Homework Equations The Attempt at a Solution I don't understand why sometimes we have a comma and sometimes we have a semi-colon. thank you

Hello, for some calculation I need the behaviour of the hypergeometric function 2F1 near z=\tfrac{1}{2}. Specifically I need _2 F_1(\mu,1-\mu,k,\tfrac{1}{2}+i x) with x\in \mathbb{R} near 0, and 1/2\leq\mu\leq 2, 1\leq k \in \mathbb{N}. Differentiating around x=0 and writing the...

I'm trying to show that: F(a, b; z) = F(a-1, b; z) + (z/b) F(a, b+1 ; z) where F(a, b; z) is Kummer's confluent hypergeometric function and F(a, b; z) = SUM[SIZE="1"]n=0[ (a)[SIZE="1"]n * z^n ] / [ (b)[SIZE="1"]n * n!] where (a)[SIZE="1"]n is the Pochhammer symbol and is...

Homework Statement I have three problems on my homework set that I can't figure out. I'll start with the longest one: Show that by letting z=\zeta^{-1} and u=\zeta^{\alpha}v(\zeta) that the hypergeometric differential equation z(1-z)\frac {d^2u}{dz^2} + \left[\gamma-(\alpha+\beta+1)z...

Hello: I need to simplify the following if possible _2F_1(a,b;c;-x^2) - _2F_1(a+1,b+1;c+1;-x^2) In fact, a= 1/2 and c=3/2 and b>=1. In other words, the difference above that I am interested in is more specifically _2F_1(.5, b; 1.5; -x^2) - _2F_1(.5+1, b+1...

hallo, i now spent an hour looking for a formula connecting the modified bessel functions I_n and K_n to the hypergeometrical series F(a,b;c;z). has somedoby an idea? thank you

Hello, Im just wondering is there a simply calculated formula for the expected value and variance for the hypergeometric distribution. I know how to do it with long calculations. I know the expected value for the binomial is = np and the variance is = npq = np(1-p) .. Is there something like...

How do you derive hypergeometirc identities of the form 2F1(a,b,c,z)= gamma function. What I mean is that the hypergeometric function converges to a set of gamme functions function in terms of (a,b,c) where z is not 1,-1, or 1/2 ? The hypergeometric identities in the mathworld summary...

How would i go about showing the special case F(1, b, b; x) of the hypergeometic function is the geometric series and also how the geometric series is = 1/ (1 -x) Cheers, Dave

[Note: P and p throughout are probabilities] Fact: The hypergeometric distribution is the precise probability of crawing from a dichotomous (S-F) population without replacement. A family of probabilistic sieves can be constructed using this fact as follows. Step 1: Suppose we know all...

I am having trouble with a problem that asks me to show that if I change the variable of integration of the following equation from t to t-1 the following http://mathworld.wolfram.com/images/equations/EulersHypergeometricTransformations/equation1.gif (disregard that z in the denominator, that...

Show directly that the set of probabilities associated with the hypergeometric distribution sum to one. => I am thinking that this tells me to prove that since this is a probability distribution function, it really should sum to 1. Is that what the problem asking me to do? =) I got...