NAME¶

std::tanh(std::complex) - std::tanh(std::complex)

Synopsis¶

Defined in header <complex>
template< class T > (since C++11)
complex<T> tanh( const complex<T>& z );

Computes complex hyperbolic tangent of a complex value z.

Parameters¶

z - complex value

Return value¶

If no errors occur, complex hyperbolic tangent of z is returned.

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

* std::tanh(std::conj(z)) == std::conj(std::tanh(z)).
* std::tanh(-z) == -std::tanh(z).
* If z is (+0,+0), the result is (+0,+0).
* If z is (x,+∞) (for any^[1] finite x), the result is (NaN,NaN) and FE_INVALID is
raised.
* If z is (x,NaN) (for any^[2] finite x), the result is (NaN,NaN) and FE_INVALID
may be raised.
* If z is (+∞,y) (for any finite positive y), the result is (1,+0).
* If z is (+∞,+∞), the result is (1,±0) (the sign of the imaginary part is
unspecified).
* If z is (+∞,NaN), the result is (1,±0) (the sign of the imaginary part is
unspecified).
* If z is (NaN,+0), the result is (NaN,+0).
* If z is (NaN,y) (for any non-zero y), the result is (NaN,NaN) and FE_INVALID may
be raised.
* If z is (NaN,NaN), the result is (NaN,NaN).
1. ↑ per C11 DR471, this only holds for non-zero x. If z is (0,∞), the result
should be (0,NaN).
2. ↑ per C11 DR471, this only holds for non-zero x. If z is (0,NaN), the result
should be (0,NaN).

Notes¶

Mathematical definition of hyperbolic tangent is tanh z =

ez
-e-z
ez
+e-z

.

Hyperbolic tangent is an analytical function on the complex plane and has no branch
cuts. It is periodic with respect to the imaginary component, with period πi, and
has poles of the first order along the imaginary line, at coordinates (0, π(1/2 +
n)). However no common floating-point representation is able to represent π/2
exactly, thus there is no value of the argument for which a pole error occurs.

Example¶

// Run this code

#include <cmath>
#include <complex>
#include <iostream>

int main()
{
std::cout << std::fixed;
std::complex<double> z(1.0, 0.0); // behaves like real tanh along the real line
std::cout << "tanh" << z << " = " << std::tanh(z)
<< " (tanh(1) = " << std::tanh(1) << ")\n";

std::complex<double> z2(0.0, 1.0); // behaves like tangent along the imaginary line
std::cout << "tanh" << z2 << " = " << std::tanh(z2)
<< " ( tan(1) = " << std::tan(1) << ")\n";
}

Output:¶

tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594)
tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408)

See also¶

computes hyperbolic sine of a complex number
sinh(std::complex) (\({\small\sinh{z}}\)sinh(z))
(function template)
computes hyperbolic cosine of a complex number
cosh(std::complex) (\({\small\cosh{z}}\)cosh(z))
(function template)
atanh(std::complex) computes area hyperbolic tangent of a complex number
(C++11) (\({\small\operatorname{artanh}{z}}\)artanh(z))
(function template)
tanh
tanhf computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x))
tanhl (function)
(C++11)
(C++11)
tanh(std::valarray) applies the function std::tanh to each element of valarray
(function template)
C documentation for
ctanh