cosh¶
- cosh(x: array, /) array ¶
Calculates an implementation-dependent approximation to the hyperbolic cosine for each element
x_i
in the input arrayx
.The mathematical definition of the hyperbolic cosine is
\[\operatorname{cosh}(x) = \frac{e^x + e^{-x}}{2}\]Note
The hyperbolic cosine is an entire function in the complex plane and has no branch cuts. The function is periodic, with period \(2\pi j\), with respect to the imaginary component.
- Parameters:
x (array) – input array whose elements each represent a hyperbolic angle. Should have a floating-point data type.
- Returns:
out (array) – an array containing the hyperbolic cosine of each element in
x
. The returned array must have a floating-point data type determined by Type Promotion Rules.
Notes
Special cases
Note
For all operands,
cosh(x)
must equalcosh(-x)
.For real-valued floating-point operands,
If
x_i
isNaN
, the result isNaN
.If
x_i
is+0
, the result is1
.If
x_i
is-0
, the result is1
.If
x_i
is+infinity
, the result is+infinity
.If
x_i
is-infinity
, the result is+infinity
.
For complex floating-point operands, let
a = real(x_i)
,b = imag(x_i)
, andNote
For complex floating-point operands,
cosh(conj(x))
must equalconj(cosh(x))
.If
a
is+0
andb
is+0
, the result is1 + 0j
.If
a
is+0
andb
is+infinity
, the result isNaN + 0j
(sign of the imaginary component is unspecified).If
a
is+0
andb
isNaN
, the result isNaN + 0j
(sign of the imaginary component is unspecified).If
a
is a nonzero finite number andb
is+infinity
, the result isNaN + NaN j
.If
a
is a nonzero finite number andb
isNaN
, the result isNaN + NaN j
.If
a
is+infinity
andb
is+0
, the result is+infinity + 0j
.If
a
is+infinity
andb
is a nonzero finite number, the result is+infinity * cis(b)
.If
a
is+infinity
andb
is+infinity
, the result is+infinity + NaN j
(sign of the real component is unspecified).If
a
is+infinity
andb
isNaN
, the result is+infinity + NaN j
.If
a
isNaN
andb
is either+0
or-0
, the result isNaN + 0j
(sign of the imaginary component is unspecified).If
a
isNaN
andb
is a nonzero finite number, the result isNaN + NaN j
.If
a
isNaN
andb
isNaN
, the result isNaN + NaN j
.
where
cis(v)
iscos(v) + sin(v)*1j
.Changed in version 2022.12: Added complex data type support.