Examples of using Hypergeometric in English and their translations into Tagalog
{-}
-
Ecclesiastic
-
Colloquial
-
Computer
Ramanujan independently discovered results of Gauss,Kummer and others on 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 her thesis she gave algorithms to find recurrence relations between sums of terms in hypergeometric series.
Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic.
He studied these special functions as arising from the solution of differential equations derived from the hypergeometric equation.
Many of Erdélyi's papers were on the hypergeometric function so it was natural for him to write to Whittaker for help.
In both the joint papers andhis 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.
There her doctoral studies were supervised by Earl Rainville who suggest that she examine some combinatorial problems related to hypergeometric series.
Fox's main contributions were on hypergeometric functions, integral transforms, integral equations and the mathematics of navigation.
Such names as Rogers- Ramanujan identities, Rogers- Ramanujan continued fractions and Rogers transformations are known in the theory of partitions,combinatorics and hypergeometric series.
Erdélyi was a leading expert on special functions,in particular hypergeometric functions, orthogonal polynomials and Lamé functions.
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.
He applied this technique systematically in a long series of papers to the study of the gamma function, hypergeometric functions, Dirichlet series, the Riemann zeta function and related number-theoretic functions.
The first of these was Some generalized hypergeometric polynomials which appeared in the Bulletin of the American Mathematical Society in 1947.
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.
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.
He continued his mathematical work, however, andat this time he worked on hypergeometric series and investigated relations between integrals and series.
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.
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.
In the last five of his papers dealing with the hypergeometric functions, Barnes made extensive use of the integrals studied by Mellin in which the integral.