Mathematical series | Ordinary differential equations | Hypergeometric functions | Factorial and binomial topics

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). Every second-order linear ODE with three regular singular points can be transformed into this equation. For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by and . There is no known system for organizing all of the identities; indeed, there is no known algorithm that can generate all identities; a number of different algorithms are known that generate different series of identities. The theory of the algorithmic discovery of identities remains an active research topic. (Wikipedia).

Hypergeometric function
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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 2

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 5

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 4

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 3

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 6

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 7

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 1

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 8

Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of

From playlist Hypergeometric Functions, Character Sums and Applications

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Introduction to Hyperbolic Functions

This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Differentiation of Hyperbolic Functions

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Masoud Kamgarpour: Langlands correspondence for hypergeometric mo-tives

30 September 2021 Abstract: Hypergeometric sheaves are rigid local systems on the punctured projective line. Their study originated in the seminal work of Riemann on the Euler{Gauss hypergeometric function and has blossomed into an active eld with connections to many areas of mathematics.

From playlist Representation theory's hidden motives (SMRI & Uni of Münster)

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Probability Theory - Part 6 - Hypergeometric Distribution [dark version]

Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.

From playlist Probability Theory [dark version]

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Francesco Mezzadri: Moments of Random Matrices and Hypergeometric Orthogonal Polynomials

We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely

From playlist Jean-Morlet Chair - Grava/Bufetov

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FoxH: A New Super Special Function

The Wolfram Language has over 250 mathematical functions, including well-known elementary and special functions. Most of these mathematical functions might be considered as specific cases of very general superfunctions like the G-function or MeijerG, which was introduced in Version 3 of Ma

From playlist Wolfram Technology Conference 2021

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Calculus 2: Hyperbolic Functions (1 of 57) What is a Hyperbolic Function? Part 1

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what are hyperbolic functions and how it compares to trig functions. Next video in the series can be seen at: https://youtu.be/c8OR8iJ-aUo

From playlist CALCULUS 2 CH 16 HYPERBOLIC FUNCTIONS

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