Heine Representations and Monotonicity Properties of Determinants and Pfaffians
Abbreviated Journal Title
Determinant; Pfaffian; Complete monotonicity; Absolute monotonicity; Orthogonal functions; TURAN TYPE INEQUALITIES; HYPERGEOMETRIC-FUNCTIONS; ORDER; Mathematics
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.
"Heine Representations and Monotonicity Properties of Determinants and Pfaffians" (2015). Faculty Bibliography 2010s. 6593.