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4.8.3 Hyperbolic functions

cl_R sinh (const cl_R& x)

Returns sinh(x).

cl_N sinh (const cl_N& z)

Returns sinh(z). The range of the result is the entire complex plane.

cl_R cosh (const cl_R& x)

Returns cosh(x). The range of the result is the interval cosh(x) >= 1.

cl_N cosh (const cl_N& z)

Returns cosh(z). The range of the result is the entire complex plane.

struct cosh_sinh_t { cl_R cosh; cl_R sinh; };
cosh_sinh_t cosh_sinh (const cl_R& x)

Returns both sinh(x) and cosh(x). This is more efficient than computing them separately. The relation cosh^2 - sinh^2 = 1 will hold only approximately.

cl_R tanh (const cl_R& x)
cl_N tanh (const cl_N& x)

Returns tanh(x) = sinh(x)/cosh(x).

cl_N asinh (const cl_N& z)

Returns arsinh(z). This is defined as arsinh(z) = log(z+sqrt(1+z^2)) and satisfies arsinh(-z) = -arsinh(z). The range of the result is the strip in the complex domain -pi/2 <= imagpart(arsinh(z)) <= pi/2, excluding the numbers with imagpart = -pi/2 and realpart > 0 and the numbers with imagpart = pi/2 and realpart < 0.

cl_N acosh (const cl_N& z)

Returns arcosh(z). This is defined as arcosh(z) = 2*log(sqrt((z+1)/2)+sqrt((z-1)/2)). The range of the result is the half-strip in the complex domain -pi < imagpart(arcosh(z)) <= pi, realpart(arcosh(z)) >= 0, excluding the numbers with realpart = 0 and -pi < imagpart < 0.

cl_N atanh (const cl_N& z)

Returns artanh(z). This is defined as artanh(z) = (log(1+z)-log(1-z)) / 2 and satisfies artanh(-z) = -artanh(z). The range of the result is the strip in the complex domain -pi/2 <= imagpart(artanh(z)) <= pi/2, excluding the numbers with imagpart = -pi/2 and realpart <= 0 and the numbers with imagpart = pi/2 and realpart >= 0.


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