Add to ORKGWe provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and Beukers-Heckman~(1989) for globally bounded and algebraic hypergeometric functions, however in a more general setting which allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.Comment: 21 page
Two theorems on the sums of generalized hypergeometric functions have been established. The theorems...
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval a...
textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a co...
AbstractFor a generalized hypergeometric function pFq[z] with positive integral differences between ...
We are going to study properties of "hypergeometrization" -- an operator which act on analytic funct...
It is well-known that differentiation of hypergeometric function multiplied by a certain power funct...
AbstractA formula for a generalized hypergeometric function pFq(2) with positive integral difference...
We derive formulas that generalize contiguity relations of Gauss hypergeometric functions to the ca...
The study of hypergeometric functions started in 1813 with a paper by Gauss. Hypergeometric function...
In an earlier paper the author has established two theorems on generalized hypergeometric functions....
AbstractA generalized hypergeometric function pFq with negative integral differences between certain...
I show that a hypergeometric function p q F (a1, . . . , ap; b1, . . . , bq; ·) with p ≤ q belongs ...
In this new version, a similar problem for G-functions is considered in Section 6.Siegel defined in ...
As a generalization of Riemann-Liouville integral, we introduce integral transformations of converge...
AbstractSummations over the positive integers n of the generalized hypergeometric expressions (±1)np...
Two theorems on the sums of generalized hypergeometric functions have been established. The theorems...
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval a...
textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a co...
AbstractFor a generalized hypergeometric function pFq[z] with positive integral differences between ...
We are going to study properties of "hypergeometrization" -- an operator which act on analytic funct...
It is well-known that differentiation of hypergeometric function multiplied by a certain power funct...
AbstractA formula for a generalized hypergeometric function pFq(2) with positive integral difference...
We derive formulas that generalize contiguity relations of Gauss hypergeometric functions to the ca...
The study of hypergeometric functions started in 1813 with a paper by Gauss. Hypergeometric function...
In an earlier paper the author has established two theorems on generalized hypergeometric functions....
AbstractA generalized hypergeometric function pFq with negative integral differences between certain...
I show that a hypergeometric function p q F (a1, . . . , ap; b1, . . . , bq; ·) with p ≤ q belongs ...
In this new version, a similar problem for G-functions is considered in Section 6.Siegel defined in ...
As a generalization of Riemann-Liouville integral, we introduce integral transformations of converge...
AbstractSummations over the positive integers n of the generalized hypergeometric expressions (±1)np...
Two theorems on the sums of generalized hypergeometric functions have been established. The theorems...
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval a...
textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a co...