For two-parameter generalized trigonometric and hyperbolic functions, the paper proves monotonicity and (log-)convexity or concavity in the parameters p and q, and derives new hypergeometric representations and integral evaluations.
On generalized trigonometric functions with two parame- ters
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A look at generalized trigonometric functions as functions of their two parameters and further new properties
For two-parameter generalized trigonometric and hyperbolic functions, the paper proves monotonicity and (log-)convexity or concavity in the parameters p and q, and derives new hypergeometric representations and integral evaluations.