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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotics of Hermite-Padé polynomials for a set of functions with different branch points (1987)
    Springer
    Constructive approximation 3 (1987), S. 13-29 
    Details
    ISSN: 1432-0940
    Keywords: Hermite-Padé ; Reproducing kernel ; Polynomial ; Asymptotic ; Integral equation ; 30E15 ; 41A21
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For an example where the functions have different branch points we derive the asymptotics of diagonal Hermite-Padé polynomials of type I. The method uses an integral equation obtained by approximating a reproducing kernel. The results are consistent with a new conjecture on the asymptotics of the polynomials associated with more general functions with different branch points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890550
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Padé polynomial asymptotics from a singular integral equation (1990)
    Springer
    Constructive approximation 6 (1990), S. 157-166 
    Details
    ISSN: 1432-0940
    Keywords: Padé approximant ; Integral equation ; Padé polynomial ; 41A21 ; 30E10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We derive a singular integral equation satisfied by the remainder function associated with the polynomials forming a diagonal Padé approximant. From this equation, the asymptotic behavior of the high-order polynomials is deduced for certain classes of functions being approximated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01889355
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Asymptotics of generalized jacobi polynomials (1986)
    Springer
    Constructive approximation 2 (1986), S. 59-77 
    Details
    ISSN: 1432-0940
    Keywords: 41A21 ; 33A65 ; Padé approximant ; Orthogonal polynomial ; Hermite-Padé polynomial ; Laguerre-Hahn polynomial ; Liouville-Green approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Polynomialsp 1,(z),p 2 (z), of degreen are defined by the relation $$p_1 (z) + p_2 (z)\prod\nolimits_{i = 1}^3 {(z - b_l )^{v_1 } } = O(z^{ - n - 1} ),z \to \infty $$ , where $$\sum\nolimits_{i = 1}^3 {v_i = 0} $$ . We obtain the asymptotic behavior of these polynomials asn→∞ and show that it agrees with a previous conjecture.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01893417
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    Paper (German National Licenses)
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