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Mostrando ítems 11-20 de 20
New series expansions for the ℋ-function of communication theory
(Taylor & Francis, 2023)
Artículo / Artikulua,
TheH-function of communication theory plays an important role inthe error rate analysis in digital communication with the presenceof additive white Gaussian noise (AWGN) and generalized multipathfading conditions. In this ...
Series representations of the Volterra function and the Fransén–Robinson constant
(Elsevier, 2021)
info:eu-repo/semantics/article,
The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only ...
Convergent expansions of the confluent hypergeometric functions in terms of elementary functions
(American Mathematical Society, 2018)
info:eu-repo/semantics/article,
We consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); ...
An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions
(Springer, 2022)
Artículo / Artikulua,
We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three ...
A convergent version of Watson’s lemma for double integrals
(Taylor & Francis, 2022)
Artículo / Artikulua,
A modification of Watson’s lemma for Laplace transforms ∞
0 f(t)
e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic
expansion for large |z| with the extra property of being convergent as well. Inspired ...
Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp
(Taylor & Francis, 2020)
info:eu-repo/semantics/article,
We derive a convergent expansion of the generalized hypergeometric function p−1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We ...
Uniform approximations of the first symmetric elliptic integral in terms of elementary functions
(Springer, 2022)
info:eu-repo/semantics/article,
We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y ...
On a particular class of Meijer's G functions appearing in fractional calculus
(Academic Publications, 2018)
info:eu-repo/semantics/article,
In this paper we investigate the Meijer G-function G p+1,p+1 p,1 which, for certain parameter values, represents the Riemann-Liouville fractional integral of the Meijer-Nørlund function G p,p. p,0 The properties of this ...
Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions
(University of Szeged (Hungría), 2020)
info:eu-repo/semantics/article,
We consider the second-order linear differential equation (x2 − 1)y'' + f (x)y′ + g(x)y = h(x) in the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet–Neumann). The ...
Analytical ray transfer matrix for the crystalline lens
(OSA Publishing, 2022)
Artículo / Artikulua,
We present the formulation of a paraxial ray transfer or ABCD matrix for onion-type
GRIN lenses. In GRIN lenses, each iso-indicial surface (IIS) can be considered a refracting
optical surface. If each IIS is a shell or ...