ad hoc methods—in some sense inspired by the Padé theory—typically replace them. Since a Padé approximant is a rational function, an artificial singular...

In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants Rm, n to a given complex formal power series...

Eugène Padé (French: [pade]; 17 December 1863 – 9 July 1953) was a French mathematician, who is now remembered mainly for his development of Padé approximation...

approximate the exponential function the best. These are known as Padé approximants. A Padé approximant with numerator of degree m and denominator of degree n is...

clever identity involving the hypergeometric function 1892 Henri Padé defined Padé approximant 1972 Bill Gosper – First exact algorithms for continued fraction...

algorithm; generalization of Euclidean algorithm and Gaussian elimination Padé approximant Schwartz–Zippel lemma and testing polynomial identities Chinese remainder...

rational interpolation is interpolation by rational functions using Padé approximant, and trigonometric interpolation is interpolation by trigonometric...

\mathbb {C} } is complex frequency. This can be approximated using a Padé approximant, as follows: e − s T = e − s T / 2 e s T / 2 ≈ 1 − s T / 2 1 + s T...

function. Mathematics portal Asymptotic expansion Newton polynomial Padé approximant – best approximation by a rational function Puiseux series – Power...

diagonal Padé approximants have trouble with the so-called evanescent modes. These evanescent modes should decay rapidly in z, but the diagonal Padé approximants...

Different approximations: Moving least squares Padé approximant Padé table — table of Padé approximants Hartogs–Rosenthal theorem — continuous functions...

real numbers by rational numbers Padé approximation, the approximation of functions obtained by set of Padé approximants Any approximation represented in...

convergence of Padé Approximants states that the diagonal and supra-diagonal Padé (or equivalently, the continued fraction approximants to the power series)...

transformations as numerical techniques. Examples of such techniques are Padé approximants, Levin-type sequence transformations, and order-dependent mappings...

Hadamard's lemma Laurent series – Power series with negative powers Padé approximant – 'Best' approximation of a function by a rational function of given...

series Function approximation Numerical analysis Orthonormal basis Padé approximant Schauder basis Kalman filter Achiezer (Akhiezer), N.I. (2013) [1956]...

notion of rational approximations of functions (nowadays known as Padé approximants), and gave the first full proof for the Cayley–Hamilton theorem. He...

Hadamard's lemma Laurent series – Power series with negative powers Padé approximant – 'Best' approximation of a function by a rational function of given...

conversely. This is used in the q-series expansion of the j-invariant. Padé approximant – Another technique used when a Taylor series is not viable. Roy, Ranjan...

diagram of the approximants to the inverse Langevin function presents the figure below. It is valid for the rational/Padé approximants, A recently published...

For equi-spaced nodes, they may be calculated efficiently as the Padé approximant of x s ⋅ ( log ⁡ x ) m {\displaystyle x^{s}\cdot (\log x)^{m}} , where...

the 17th century, long before Olbers was born. Padé approximant: named after and developed by Henri Padé around 1890, but was first introduced by Ferdinand...

fraction among the a i / b i {\displaystyle a_{i}/b_{i}} . Mediant Padé approximant Stern–Brocot tree Parallel (operator) Milburn, R. M. (1880). Mathematical...

Madhava of Sangamagrama Madhava's sine table Madhava's correction term Padé approximant Taylor series Laurent series Puiseux series Gupta 1987; Katz 1995;...

} The generalized Shanks transformation is closely related to Padé approximants and Padé tables. Note: The calculation of determinants requires many arithmetic...

Gonchar's research focused on Padé approximants (specifically the relation between the convergence of the Padé approximants and the analytic properties...

interpolation and approximation of functions, for example the Padé approximants introduced by Henri Padé. Approximations in terms of rational functions are well...

the initial data. Also, one may use sequence transformations like Padé approximants and Levin-type sequence transformations as extrapolation methods that...

original series. Examples of such nonlinear sequence transformations are Padé approximants, the Shanks transformation, and Levin-type sequence transformations...

to the Nyquist frequency. The bilinear transform is a first-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane...