HYPERGEOMETRIC TYPE INTEGRALTRANSFORMS ON THE SPACE L ;r

H-Transforms ◽  
2004 ◽  
pp. 214-272
Keyword(s):  
Hypergeometric Type

scholarly journals Hypergeometric type identities in the $p$-adic setting and modular forms

2015 ◽  
Vol 144 (4) ◽  
pp. 1493-1508 ◽  
Author(s):  
Jenny G. Fuselier ◽  
Dermot McCarthy
Keyword(s):  
Modular Forms ◽  
Hypergeometric Type

Supercongruences Occurred to Rigid Hypergeometric Type Calabi–Yau Threefolds

2019 ◽  
pp. 467-470
Author(s):  
Ling Long ◽  
Fang-Ting Tu ◽  
Noriko Yui ◽  
Wadim Zudilin
Keyword(s):  
Hypergeometric Type

scholarly journals On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 47 ◽  
Author(s):  
Mama Foupouagnigni ◽  
Salifou Mboutngam
Keyword(s):  
Difference Equation ◽  
Divided Difference ◽  
Polynomial Solution ◽  
Formal Proof ◽  
Second Order ◽  
Fixed Degree ◽  
Hypergeometric Type ◽  
The Mean ◽  
The Right

In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, difference or q-difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the divided-difference operator as well as by defining explicitly, the right and the “left” inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution—non polynomial solution—of a second-order divided-difference equation of hypergeometric type.

scholarly journals DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

2004 ◽  
Vol 15 (09) ◽  
pp. 959-965 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Difference Equation ◽  
Jones Polynomial ◽  
Order Difference ◽  
Colored Jones Polynomial ◽  
First Order ◽  
Torus Knot ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Hypergeometric Type ◽  
The Difference

We prove that the N-colored Jones polynomial for the torus knot [Formula: see text] satisfies the second order difference equation, which reduces to the first order difference equation for a case of [Formula: see text]. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for [Formula: see text].

The analysis of point quadrat data

1956 ◽  
Vol 4 (2) ◽  
pp. 167 ◽  
Author(s):  
CD Kemp ◽  
AW Kemp
Keyword(s):  
Optimum Number ◽  
Percentage Cover ◽  
Hypergeometric Type ◽  
Point Quadrat ◽  
Theoretical Considerations ◽  
Angular Transformation

The type of distribution followed by point quadrat percentage-cover data has been studied. The hypergeometric type IIA distribution with constant n has been deduced from theoretical considerations and found to give a good fit to data published by Goodall in 1952. The parameters of this distribution assist the study not only of the overall percentage cover but also of the patchiness of the vegetation. The assumption of this type of distribution does not preclude the use of the angular transformation; this remains the appropriate transformation for stabilizing the variance. Theoretical considerations have been put forward in support of the policy of reducing the number of pins per frame. However, if this is done, the number of necessary locations is increased; only by practical experimentation can the optimum number of pins per frame be determined.

scholarly journals Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

1987 ◽  
Vol 106 ◽  
pp. 1-28 ◽  
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Linear Operators ◽  
Coefficient Estimates ◽  
Hadamard Products ◽  
Generalized Hypergeometric Functions ◽  
Hypergeometric Type ◽  
Distortion Theorems ◽  
Characterization Theorems

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

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