A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell [PDF]
, 2010 We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors.
Andrews G E +12 more
core +3 more sources
Computing hypergeometric functions rigorously [PDF]
, 2016 We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and ...
Johansson, Fredrik
core +5 more sources
An extension of beta function, its statistical distribution, and associated fractional operator
Advances in Difference Equations, 2020 Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various ...
Ankita Chandola +3 more
doaj +1 more source
Pricing Step Options under the CEV and other Solvable Diffusion Models [PDF]
, 2013 We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)].
Campolieti, Giuseppe +2 more
core +1 more source
Extende beta, hypergeometric and confluent hypergeometric functions
, 2019 15 ...
Khan, N. U., Usman, T., Aman, M.
openaire +2 more sources
A new generalization of confluent hypergeometric function and whittaker function
, 2018 In this article, we introduce a further generalizations of the confluent hypergeometric function and Whittaker function by introducing an extra parameter in the extended con uent hypergeometric function dened by Parmar [15].
N. Khan, T. Usman, M. Ghayasuddin
semanticscholar +1 more source
Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation
, 2015 We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method.
D. Demirhan +6 more
core +1 more source
Non-Integrability of Some Higher-Order Painlev\'e Equations in the Sense of Liouville [PDF]
, 2015 In this paper we study the equation $$ w^{(4)} = 5 w" (w^2 - w') + 5 w (w')^2 - w^5 + (\lambda z + \alpha)w + \gamma, $$ which is one of the higher-order Painlev\'e equations (i.e., equations in the polynomial class having the Painlev\'e property).
Christov, Ognyan, Georgiev, Georgi
core +2 more sources
Generalized Laplace transform with matrix variables
International Journal of Mathematics and Mathematical Sciences, 1987 In the present paper we have extended generalized Laplace transforms of Joshi to the space of m×m symmetric matrices using the confluent hypergeometric function of matrix argument defined by Herz as kernel.
R. M. Joshi, J. M. C. Joshi
doaj +1 more source
Properties and Applications of Extended Hypergeometric Functions
Ingeniería y Ciencia, 2014 In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions.
Daya Krishna Nagar +2 more
doaj +1 more source