naginterfaces.library.specfun.cosh

naginterfaces.library.specfun.cosh(x)

cosh returns the value of the hyperbolic cosine, $\cosh \left(x\right)$.

For full information please refer to the NAG Library document for s10ac

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/s/s10acf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

chxfloat

The value of the hyperbolic cosine, $\cosh \left(x\right)$.

Warns

NagAlgorithmicWarning

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $\left|x\right|\le E_1$.

The function has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of $\cosh \left(x\right)$ at the nearest valid argument.

Notes

cosh calculates an approximate value for the hyperbolic cosine, $\cosh \left(x\right)$.

For $\left|x\right|\le E_1\text{,}\cosh \left(x\right)=\frac{1}{2}(e^x+e^{-x})$.

For $\left|x\right|>E_1$, the function fails owing to danger of setting overflow in calculating $e^x$. The result returned for such calls is $\cosh \left(E_1\right)$, i.e., it returns the result for the nearest valid argument.

References

NIST Digital Library of Mathematical Functions