Heine Representations and Monotonicity Properties of Determinants and Pfaffians

    Authors

    M. E. H. Ismail;P. Simeonov

    Comments

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    Abbreviated Journal Title

    Constr. Approx.

    Keywords

    Determinant; Pfaffian; Complete monotonicity; Absolute monotonicity; Orthogonal functions; TURAN TYPE INEQUALITIES; HYPERGEOMETRIC-FUNCTIONS; ORDER; Mathematics

    Abstract

    We establish integral representations of Heine type for certain integrals of determinants. We use these representations to derive monotonicity properties of such determinants. New integral representations of Heine type for biorthogonal functions obtained from the general Gram-Schmidt orthonormalization process are given. We also establish the monotonicity of certain Pfaffians using the de Bruijn formula of Ishikawa and Zeng. The complete or absolute monotonicity of a number of Pfaffian functions is established.

    Journal Title

    Constructive Approximation

    Volume

    41

    Issue/Number

    2

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    231

    Last Page

    249

    WOS Identifier

    WOS:000350305000003

    ISSN

    0176-4276

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