scholarly journals Periods of Hodge cycles and special values of the Gauss' hypergeometric function

2021 ◽  
Author(s):  
Jorge Duque Franco
Keyword(s):  
Hypergeometric Function ◽  
Gauss Hypergeometric Function ◽  
Special Values

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

Analytic expressions for annuities based on Makeham–Beard mortality laws

2020 ◽  
pp. 1-13
Author(s):  
David C. Bowie
Keyword(s):  
Hypergeometric Function ◽  
Mortality Rates ◽  
Gauss Hypergeometric Function ◽  
Mortality Data ◽  
Exponential Increase ◽  
Analytic Expressions ◽  
Life Annuities ◽  
Appell Function

Abstract This note derives analytic expressions for annuities based on a class of parametric mortality “laws” (the so-called Makeham–Beard family) that includes a logistic form that models a decelerating increase in mortality rates at the higher ages. Such models have been shown to provide a better fit to pensioner and annuitant mortality data than those that include an exponential increase. The expressions derived for evaluating single life and joint life annuities for the Makeham–Beard family of mortality laws use the Gauss hypergeometric function and Appell function of the first kind, respectively.

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals On weighted inequalities for certain fractional integral operators

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
R. K. Raina
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Weighted Inequalities ◽  
Fractional Integral Operators

This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.

scholarly journals ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS

2007 ◽  
Vol 49 (1) ◽  
pp. 45-52 ◽  
Author(s):  
STEPHAN RUSCHEWEYH ◽  
LUIS SALINAS
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Boundary Point ◽  
Univalent Functions ◽  
Gegenbauer Polynomials ◽  
Gauss Hypergeometric Function ◽  
Coefficient Estimates ◽  
Image Position

Abstract.D. Brannan's conjecture says that for 0 <α,β≤1, |x|=1, and n∈N one has |A2n−1(α,β,x)|≤|A2n−1(α,β,1)|, where We prove this for the case α=β, and also prove a differentiated version of the Brannan conjecture. This has applications to estimates for Gegenbauer polynomials and also to coefficient estimates for univalent functions in the unit disk that are ‘starlike with respect to a boundary point’. The latter application has previously been conjectured by H. Silverman and E. Silvia. The proofs make use of various properties of the Gauss hypergeometric function.

Sign in / Sign up

Export Citation Format

Share Document