engleski

Hilbert inequality and Gaussian hypergeometric functions

By using the integral representation of Gaussian hypergeometric function, we obtain Hilbert type inequalities with some fractional kernels and non-conjugate parameters. Such inequalities include the constant factors expressed in terms of hypergeometric functions. Further, we obtain the best possible constants for some general cases, in conjugate case.

inequalities; Hilbert type inequality; Hardy-Hilbert type inequality; equivalent inequalities; non-conjugate parameters; beta function; gamma function; the best possible constant; hypergeometric function; Gaussian hypergeometric function; Pfaff's reflection law; Euler identity

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