> i am trying to define sinh ,cosh, tanh , coth , in gsl library...

If you're looking for real-valued hyperbolic functions, your
compiler's standard math.h header should have most of what you need:
https://secure.wikimedia.org/wikipedia/en/wiki/Math.h.  Some things,
e.g. coth, you may need to reexpress using other functions.  You may
find some related elementary functions in GSL listed here:
https://www.gnu.org/s/gsl/manual/html_node/Elementary-Functions.html.

If you're looking for complex-valued hyperbolic functions, I think you
want this portion of the manual:
https://www.gnu.org/s/gsl/manual/html_node/Complex-Hyperbolic-Functions.html

Hope that helps,
Rhys

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