scholarly journals Zeros of a cross-product of the Coulomb wave and Tricomi hypergeometric functions

2016 ◽  
Vol 145 (4) ◽  
pp. 1643-1648
Author(s):  
Árpád Baricz
Keyword(s):  
Hypergeometric Functions ◽  
Cross Product

Acoustical Properties of Speech as Indicators of Depression and Suicidal Risk

2008 ◽  
Vol 4 ◽  
Author(s):  
Michael Joshua Landau
Keyword(s):  
Multiple Regression ◽  
Energy Band ◽  
Mental States ◽  
Cross Product ◽  
Female Group ◽  
Suicidal Risk ◽  
Energy Bands ◽  
Band Ratio ◽  
Acoustical Properties ◽  
Male Group

Acoustical properties of speech have been shown to be related to mental states such as remission and depression. The objective of this project was to relate the energy in frequency bands with the severity of the mental state using the Beck Depression Inventory (BDI). Recorded speech was obtained from male and female subjects with mental states of remission, depression, and suicidal risk. These subjects had recorded automated and spontaneous speech samples. Multiple regression analysis was used to relate the independent energy band ratio variables with the dependent BDI scores, and thus allow the determination of equitable BDI scores for future patients. For the male group, the square of the 3rd energy band and the cross-product of the 2nd and 3rd energy band were prominent in both the reading and interviewed groups. Therefore the equation with the 2nd lowest Akaike Information Criterion (AIC) score was chosen for the reading male group, and the 1st lowest AIC score was chosen for the interviewed male group. For the female group, the square and cross-product of the 1st and 2nd energy bands were prominent in both the reading and interviewed groups. Therefore the 2nd lowest AIC score was chosen for the reading female group, and the 1st lowest AIC score was chosen for the interviewed female group. The clinician could thus determine the patient’s mood or state of mind by comparing the estimated BDI score with the ranges of total BDI scores: remitted 0 – 20, depressed 15 – 38, suicidal 38 – 46. Keywords: speech, mental states, power spectra, multiple regression, information theoretic criterion

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals New Specific and General Linearization Formulas of Some Classes of Jacobi Polynomials

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 74
Author(s):  
Waleed Mohamed Abd-Elhameed ◽  
Afnan Ali
Keyword(s):  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Algebraic Computation ◽  
Ultraspherical Polynomials ◽  
Current Article ◽  
Linearization Coefficients

The main purpose of the current article is to develop new specific and general linearization formulas of some classes of Jacobi polynomials. The basic idea behind the derivation of these formulas is based on reducing the linearization coefficients which are represented in terms of the Kampé de Fériet function for some particular choices of the involved parameters. In some cases, the required reduction is performed with the aid of some standard reduction formulas for certain hypergeometric functions of unit argument, while, in other cases, the reduction cannot be done via standard formulas, so we resort to certain symbolic algebraic computation, and specifically the algorithms of Zeilberger, Petkovsek, and van Hoeij. Some new linearization formulas of ultraspherical polynomials and third-and fourth-kinds Chebyshev polynomials are established.

scholarly journals A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1161
Author(s):  
Hari Mohan Srivastava ◽  
Sama Arjika
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Additional Parameter ◽  
Physical Sciences ◽  
General Family ◽  
Hypergeometric Polynomials

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.

Sign in / Sign up

Export Citation Format

Share Document