Examples of using Hypergeometric in English and their translations into Korean
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For far too long, there has been a dearth of good references on basic hypergeometric series.
For example he expanded hypergeometric functions in series of Laguerre and Hermite polynomials.
The paper was On a generalisation of Riemann 's problem concerning hypergeometric functions.
He published a paper on hypergeometric series in Crelle's Journal in 1836 and he sent a copy of the paper to Jacobi.
In both the joint papers and his single author papers he wrote on differential equations, hypergeometric functions and Bessel functions.
He extended Gauss 's work on hypergeometric series, giving developments that are useful in the theory of differential equations.
This is a very personal book, a distillation of those results in basic hypergeometric series which hold the most appeal to its author.
The present book and Basic hypergeometric series by G Gasper and M Rahman have appeared in the past two years to greatly rectify this situation.
Erdélyi was a leading expert on special functions,in particular hypergeometric functions, orthogonal polynomials and Lamé functions.
Such names as Rogers- Ramanujan identities, Rogers- Ramanujan continued fractions andRogers transformations are known in the theory of partitions, combinatorics and hypergeometric series.
Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic.
In the book hypergeometric functions, Bessel functions, the Jacobi orthogonal polynomials, the Hahn orthogonal polynomials, Laguerre polynomials, Hermite polynomials, Meixner polynomials, Krawtchouk polynomials and Charlier polynomials all play their part in addition to other orthogonal polynomials and special functions.
Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function.
The first of these was Some generalized hypergeometric polynomials which appeared in the Bulletin of the American Mathematical Society in 1947.
His work is important in the development of the theory of functions, in particular having applications in the theory of hypergeometric series and differential equations.
The distributions are the binomial, geometric, hypergeometric, negative binomial, beta-binomial, multinomial, and Poisson.
His last mathematical paper, published in 1910, was a short andelegant demonstration of a previously known result of Thomae concerning a transformation of a generalised hypergeometric function of unit argument into a more rapidly convergent function of the same kind.
His early work on Bessel functions and hypergeometric functions appeared in his first major text Integrals of Bessel functions which was published in 1962.
He continued his mathematical work,however, and at this time he worked on hypergeometric series and investigated relations between integrals and series.
It is a type of generalisation of a hypergeometric function and related ideas can be found in the work of Pincherle, Mellin, Ferrar, Bochner and others.
We became somewhat diverted while looking at Fine's text Basic hypergeometric series and applications when we began to look at Andrews' Introduction.
In answering the problem of when Gauss 's hypergeometric series was an algebraic function Schwarz, as he had done so many times, developed a method which would lead to much more general results.
He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society.
