Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative [PDF]
Numer. Funct. Anal. Optim. 33 (2012), no. 3, 301--319, 2011 We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given.
Almeida, R. +2 more
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Approximate closed-form formulas for the zeros of the Bessel Polynomials [PDF]
, 2011 We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex ...
Calderon, Marisol L., Campos, Rafael G.
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Series expansions for the third incomplete elliptic integral via partial fraction decompositions [PDF]
, 2006 We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic singularity $(
A. Savenkova +10 more
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Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion [PDF]
, 2002 The use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders (Kia(x)) near the transition point x=a, is discussed. In A.
Amparo Gil +9 more
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An advanced variant of an interpolatory graphical display algorithm [PDF]
, 2004 In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal.
ALA, Guido +4 more
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Fractional order optimal control problems with free terminal time [PDF]
, 2013 We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free.
A. A. Kilbas +23 more
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Approximation of fractional integrals by means of derivatives [PDF]
, 2012 We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class C-n, n is an element of N, and allow us to develop suitable
Almeida, R. +2 more
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Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
, 2015 We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials.
Exl, Lukas +2 more
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Some new series for $1/\pi$ and related congruences [PDF]
, 2016 In this paper we prove some new series for $1/\pi$ as well as related congruences. We also raise several new kinds of series for $1/\pi$ and present some related conjectural congruences involving representations of primes by binary quadratic forms ...
Sun, Zhi-Wei
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Computing the Gamma function using contour integrals and rational approximations [PDF]
, 2005 Some of the best methods for computing the gamma function are based on numerical evaluation of Hankel's contour integral. For example, Temme evaluates this integral based on steepest-decent contours by the trapezoid rule.
Schmelzer, Thomas, Trefethen, Lloyd N.
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