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Uniform convergent expansions of the error function in terms of elementary functions
(Springer, 2023)
Artículo / Artikulua,
We derive a new analytic representation of the error function erfz
in the form of a convergent series whose terms are exponential and rational functions. The expansion holds uniformly in z in the double sector | arg (±z) ...
Uniform convergent expansions of integral transforms
(American Mathematical Society, 2021)
info:eu-repo/semantics/article,
Several convergent expansions are available for most of the special functions of the mathematical physics, as well as some asymptotic expansions [NIST Handbook of Mathematical Functions, 2010]. Usually, both type of ...
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 ...
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 ...
A convergent and asymptotic Laplace method for integrals
(Elsevier, 2023)
Artículo / Artikulua,
Watson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F (z) := ∫ ∞
0
e
−zf (t)
g(t)dt for large values of the parameter z. They are useful
tools in the asymptotic approximation of ...
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 ...
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 ...