Web23 apr. 2024 · A (generalized) hypergeometric series is a power series ∞ ∑ k = 0akxk where k ↦ ak + 1 /ak is a rational function (that is, a ratio of polynomials). Many of the basic power series studied in calculus are hypergeometric series, including the ordinary geometric series and the exponential series. WebRecently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ2. We construct intriguing series …
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Webis the generalized hypergeometric function . Details Examples open all Basic Examples (5) Evaluate numerically: In [1]:= Out [1]= Plot over a subset of the reals: In [1]:= Out [1]= Evaluate symbolically: In [1]:= Out [1]= Series expansion at the origin: In [1]:= Out [1]= Series expansion at Infinity: In [1]:= Out [1]= Scope (33) Applications (6) Web13 apr. 2024 · [Show full abstract] numbers and generalized harmonic numbers by applying an algorithmic method to a known summation formula for the hypergeometric function 5F4(1). View full-text. huren houthavens
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Web8 aug. 2024 · The hypergeometric series is actually a solution of the differential equation. x(1 − x)y′′ + [γ − (α + β + 1)x]y′ − αβy = 0. This equation was first introduced by Euler … Web6 mrt. 2024 · Complex color plot of the Laguerre polynomial L n (x) with n as -1 divided by 9 and x as z to the power of 4 from -2-2i to 2+2i. In mathematics, the Laguerre … WebThe Hypergeometric and generalized hypergeometric functions as defined by Abramowitz and Stegun. Function hypergeo () is the user interface to the majority of the package functionality; it dispatches to one of a number of subsidiary functions. Usage hypergeo (A, B, C, z, tol = 0, maxiter=2000) Arguments A,B,C Parameters for hypergeo () z huren little c