Hypergeometric functions | Q-analogs
In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio of successive terms xn+1/xn is a rational function of n. If the ratio of successive terms is a rational function of qn, then the series is called a basic hypergeometric series. The number q is called the base. The basic hypergeometric series was first considered by Eduard Heine. It becomes the hypergeometric series in the limit when base . (Wikipedia).
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
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
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
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
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
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
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
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
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
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)
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
Maxim Kontsevich - An Update on Algebraic Hypergeometric Series
Algebraic hypergeometric series in one variable were classified in 1989 by F. Beukers and G. Heckman, in terms of finite complex reflection groups. Recently, K. Penson observed that one of such series is a generating series of a probability density with compact support, given again by an a
From playlist Combinatorics and Arithmetic for Physics: special days
Pure and applied geometry--understanding the continuum | Universal Hyperbolic Geometry 20
The distinction between pure and applied geometry is closely related to the difference between rational numbers and decimal numbers. Especially when we treat decimal numbers in an approximate way: specifying rather an interval or range rather than a particular value. This gives us a way of
From playlist Universal Hyperbolic Geometry