Padé approximants to certain elliptic-type functions
نویسندگان
چکیده
منابع مشابه
Padé Approximants to Certain Elliptic-type Functions
Given non-collinear points a1, a2, a3, there is a unique compact ∆ ⊂ C that has minimal logarithmic capacity among all continua joining a1, a2, and a3. For a complex-valued non-vanishing Dinicontinuous function h on∆, we define fh (z) := 1 πi ∫ ∆ h(t ) t − z d t w+(t ) ,
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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...
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The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers.
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2013
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-013-0027-9