Results 41 to 50 of about 81,111 (274)
, 2015 This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
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Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions
, 2016 In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions.
Yaşar, Banu Yılmaz +1 more
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On polynomials connected to powers of Bessel functions
, 2013 The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of
Moll, Victor H., Vignat, C.
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Table of Modified Bessel Functions
Mathematics of Computation, 1970 Abstract : The report contains 15 place tables of the modified Bessel Functions I sub zero (x), I sub one (x), ((e to the power minus x)I sub zero (x)), ((e to the power minus x) I sub one (x)), for x = 0(001)10.
J. W. W. +2 more
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Stabilization of the Benzene Radical Trianion in an Inverse‐Sandwich Yttrium Complex
Angewandte Chemie, EarlyView.A new type of benzene anion state is born: The unprecedented benzene radical trianion embedded in an inverse‐sandwich yttrium complex was synthesized by a one‐electron chemical reduction of its benzene dianion precursor using potassium graphite in the presence of [2.2.2]‐cryptand.
Weiqing Mao +5 more
wiley +2 more sources
Mathieu functions and its useful approximation for elliptical waveguides
EPJ Web of Conferences, 2017 The standard form of the Mathieu differential equation is d2ydη2+(a−2qcos2η)y=0 where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and ...
Pillay Shamini, Kumar Deepak
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Generation of Localised Vertical Streams in Unstable Stratified Atmosphere
Fluids, 2021 A new model of axially symmetric concentrated vortex generation was developed herein. In this work, the solution of a nonlinear equation for internal gravity waves in an unstable stratified atmosphere was obtained and analysed in the framework of ideal ...
Oleg Onishchenko +4 more
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Radial Covariance Functions Motivated by Spatial Random Field Models with Local Interactions
, 2014 We derive explicit expressions for a family of radially symmetric, non-differentiable, Spartan covariance functions in $\mathbb{R}^2$ that involve the modified Bessel function of the second kind. In addition to the characteristic length and the amplitude
Hristopulos, Dionissios T.
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Peptide Sequencing With Single Acid Resolution Using a Sub‐Nanometer Diameter Pore
Advanced Functional Materials, EarlyView.To sequence a single molecule of Aβ1−42–sodium dodecyl sulfate (SDS), the aggregate is forced through a sub‐nanopore 0.4 nm in diameter spanning a 4.0 nm thick membrane. The figure is a visual molecular dynamics (VMD) snapshot depicting the translocation of Aβ1−42–SDS through the pore; only the peptide, the SDS, the Na+ (yellow/green) and Cl− (cyan ...
Apurba Paul +8 more
wiley +1 more source
Results in Physics, 2018 Simple analytic approximations valid for x⩾0 have been found for the modified Bessel functions I2(x) and I2/3(x), used amply in Electromagnetism and Mechanics applications.
Pablo Martin +3 more
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