Master Theorems for a Family of Integrals

A family of general Master theorems for analytic integration over the real (or imaginary) axis with various reciprocal hyperbolic (trig) kernels ($\sinh and/or \cosh$) with varying arguments is developed. Several examples involving closed-form integrations which do not appear to exist in the standard tables are given in detail and general results are listed in an Appendix. As well, it is shown how to convert the special case of an infinite series involving ratios of Gamma functions into a finite series.