(1999): "An introduction to hypergeometric functions for economists," Econometric Reviews, 18, 287-330.Abadir, K.M.: An introduction to hypergeometric functions for economists. Econom. Rev. 18 , 287–330 (1999)
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Legendre Functions -- XVI. The Confluent Hypergeometric Function -- XVII. Bessel Functions -- XVIII. The Equations of Mathematical Physics -- XIX. Mathieu Functions -- XX. Elliptic Functions. General theorems and the Weierstrassian Functions -- XXI. The Theta Functions -- XXII. The Jacobian ...
2 Hypergeometric functions The hypergeometric function is one of the most important special functions, because of its many connections to other classes of special functions, and its numerous identities and expressions in terms of series and integrals. Definition 2.1. For parameters a,b,c∈C with c...
It is still possible, though, for some functions to form a field that has properties similar to the elementary differential field; for example, both the derivatives and the antiderivatives of a hypergeometric function is still expressible in terms of hypergeometric functions with algebraic operations...
If α, β, and γ are integers, the hypergeometric differential equation always has a solution that is regular for z = 0 and that is of the form R1(z)+ln(1−z)R2(z),where R1(z) and R2(z) are rational functions of z. To get a solution of this form, we need to apply formu...
Here, M(a, b, x) is a confluent hypergeometric function and Jl+(k) is the Jost function, which is given by: ΓΓJl+(k)=ile−πz2k Γ(2l+2)(2k)l+1 Γ(l+1−izk) (10) A factor (12kπ)12 occurs due to normalization to an energy delta function as follows: ΨΨ∫r2dr...
using common statistical methods (egχ2, Fisher's exact test, binomial probability or hypergeometric distribution), it is possible to determine that kinases are enriched in the gene list and therefore have important functions in the biological study undertaken[3]....
We tested Gpufit by using the software to process randomized simulated datasets. The precision and accuracy of the fit results, as well as the number of fit iterations and the execution time, were measured. The input data consisted of 2D Gaussian functions defined by five parameters (see Support...
An Introduction to the Mathematics and Methods of Astrodynamics , Revised Edition The fundamental mathematical principles of celestial mechanics and space navigation are presented in an introduction for students of aerospace engineering and science. Chapters are devoted to hypergeometric functions and elliptic...