sinh

sinh(x: array, /) → array

Calculates an implementation-dependent approximation to the hyperbolic sine for each element x_i of the input array x.

The mathematical definition of the hyperbolic sine is

\[\operatorname{sinh}(x) = \frac{e^x - e^{-x}}{2}\]

Note

The hyperbolic sine 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 sine 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, sinh(x) must equal -sinh(-x).

For real-valued floating-point operands,

  • If x_i is NaN, the result is NaN.

  • If x_i is +0, the result is +0.

  • If x_i is -0, the result is -0.

  • 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), and

Note

For complex floating-point operands, sinh(conj(x)) must equal conj(sinh(x)).

  • If a is +0 and b is +0, the result is +0 + 0j.

  • If a is +0 and b is +infinity, the result is 0 + NaN j (sign of the real component is unspecified).

  • If a is +0 and b is NaN, the result is 0 + NaN j (sign of the real component is unspecified).

  • If a is a positive (i.e., greater than 0) finite number and b is +infinity, the result is NaN + NaN j.

  • If a is a positive (i.e., greater than 0) finite number and b is NaN, the result is NaN + NaN j.

  • If a is +infinity and b is +0, the result is +infinity + 0j.

  • If a is +infinity and b is a positive finite number, the result is +infinity * cis(b).

  • If a is +infinity and b is +infinity, the result is infinity + NaN j (sign of the real component is unspecified).

  • If a is +infinity and b is NaN, the result is infinity + NaN j (sign of the real component is unspecified).

  • If a is NaN and b is +0, the result is NaN + 0j.

  • If a is NaN and b is a nonzero finite number, the result is NaN + NaN j.

  • If a is NaN and b is NaN, the result is NaN + NaN j.

where cis(v) is cos(v) + sin(v)*1j.

Changed in version 2022.12: Added complex data type support.