منابع مشابه
General order multivariate Padé approximants for Pseudo-multivariate functions. II
Explicit formulas for general order multivariate Padé approximants of pseudo-multivariate functions are constructed on specific index sets. Examples include the multivariate forms of the exponential function E (x) = ∞ ∑ j1,j2,...,jm=0 x1 1 x j2 2 · · ·x jm m (j1 + j2 + · · ·+ jm)! , the logarithm function L(x) = ∑ j1+j2+···+jm≥1 x1 1 x j2 2 · · ·x jm m j1 + j2 + · · ·+ jm , the Lauricella funct...
متن کاملGeneral order multivariate Padé approximants for pseudo-multivariate functions
Although general order multivariate Padé approximants were introduced some decades ago, very few explicit formulas for special functions have been given. We explicitly construct some general order multivariate Padé approximants to the class of so-called pseudo-multivariate functions, using the Padé approximants to their univariate versions. We also prove that the constructed approximants inheri...
متن کاملExploring multivariate Padé approximants for multiple hypergeometric series
We investigate the approximation of some hypergeometric functions of two variables, namely the Appell functions Fi, i = 1, . . . , 4, by multivariate Padé approximants. Section 1 reviews the results that exist for the projection of the Fi onto x = 0 or y = 0, namely, the Gauss function 2F1(a, b; c; z), since a great deal is known about Padé approximants for this hypergeometric series. Section 2...
متن کاملPadé Approximants in Complex Points Revisited
In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...
متن کاملConvergence of Multipoint Padé-type Approximants
Let µ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90041-0