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Properties of a subclass of starlike functions involving the quantum derivative operator. [PDF]

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Breaz D, Karthikeyan KR, Senguttuvan A, Mohankumar D.   +3 more
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Eukaryotic secreted proteins are encoded in repeat-rich genomic regions

Farrer RA.
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Extended hypergeometric and confluent hypergeometric functions

Applied Mathematics and Computation, 2004
The functions under consideration are the extended Gaussian hypergeometric function \[ F_p(a,b;c,z)= {1\over B(b,c- b)} \int^1_0 t^{b-1}(1- t)^{c-b-1}(1- zt)^{-a}\exp\Biggl[-{p\over t(1- t)}\Biggr]\,dt \] and its confluent counterpart \(\Phi_p(b;c;z)\) with \(\exp(zt)\) in place of \((1- zt)^{-a}\). The authors discuss differentiation with respect to \(
M. Aslam Chaudhry, Asghar Qadir, H. M. Srivastava 0001, R. B. Paris   +3 more
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The hyperbolic–hypergeometric functions

Journal of Mathematical Physics, 2001
In this work we present a new function to represent the approximate solution of a system of three charged particles. This function is based on an extension to two variables of the confluent hypergeometric function 1F1 of Kummer and can be obtained using a method similar to that used by Appell and Kampé de Fériet.
Gasaneo, G., Colavecchia, F. D., Otranto, S., Garibotti, C. R.   +3 more
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Operator Hypergeometric Functions

Journal of Mathematical Sciences, 2023
The paper deals with differential equations \[ Du=Au\tag{1} \] with a differential operator \(D\) and unbounded operator coefficients \(A\). If the case when the Cauchy problem for equation (1) is uniformly well-posed then its solution can be represented via transformation operator.
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The hypergeometric function, the confluent hypergeometric function and WKB solutions

Journal of the Mathematical Society of Japan, 2021
Take the Gauss hypergeometric equation and instead of parameters \(a,b,c\) let us write \(a=\alpha_0+\alpha \eta, b=\beta_0+\beta\eta, c=\gamma_0+\gamma\eta\) and instead of the unknown function \(w\) let us take \(w=x^{-c/2}(1-x)^{(-1/2)(a+b-c+1)}\psi\). Then the equation is written in the form \[ (-\frac{d^2}{dx^2}+\eta^2Q)\psi=0,\quad Q=\sum_{j=0}^N
Aoki, Takashi, Takahashi, Toshinori, Tanda, Mika   +2 more
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ON q-HYPERGEOMETRIC FUNCTIONS

Far East Journal of Mathematical Sciences (FJMS), 2017
Summary: In this article, we study some results on meromorphic functions defined by \(q\)-hypergeometric functions. In addition, certain sufficient conditions for these meromorphic functions to satisfy a subordination property are also pointed out. In fact, these results extend known results of starlikeness, convexity, and close to convexity.
Challab, K. A., Darus, M., Ghanim, F.
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PATH HYPERGEOMETRIC FUNCTIONS

Journal of Algebra and Its Applications, 2007
Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero–Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function.
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Zeros of Hypergeometric Functions

Computational Methods and Function Theory, 2001
Here it is shown that the hypergeometric function \(F(a,b;b+1;z)\) has no zeros in a specified half-plane for certain ranges of parameters. It is also shown that the zeros of the hypergeometric polynomials \(F(-n,kn+ \ell+1; kn+ \ell+2;z)\) cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
Boggs, Kathryn, Duren, Peter
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EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS

The Quarterly Journal of Mathematics, 1942
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