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MATHEMATICA GUIDE
Hyperbolic Functions
Mathematica supports hyperbolic functions everywhere in the complex plane—with careful attention to branch cuts—and provides an extensive web of exact and algebraic transformations, together with efficient arbitrary-precision numerical evaluation.
Reference
Sinh ▪ Cosh ▪ Tanh ▪ Csch ▪ Sech ▪ Coth
ArcSinh ▪ ArcCosh ▪ ArcTanh ▪ ArcCsch ▪ ArcSech ▪ ArcCoth
Gudermannian ▪ InverseGudermannian
I (
) — 
, entered as EsciiEsc ("imaginary i")
FullSimplify — simplify hyperbolic function expressions
FunctionExpand — reduce to algebraic forms or simpler arguments
TrigToExp, ExpToTrig — convert between hyperbolic and exponential functions
ComplexExpand — expand into real and imaginary parts
