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In general, the complex inverse hyperbolic functions can be expressed in terms of the complex square root and logarithmic
function. The complex inverse Sinh function can be expressed in the following equation:
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arcsin h(z) = log( z + √(1 + z)2) |
This being the case, an Asinh method can be implemented and added to the KMP library as follows:
public static Complex Asinh(Complex c)
{
return log(c + Sqrt(1.0 * c));
}
Inverse Hyperbolic Cosine Function
Similar to the case of the complex Asinh function, a complex Acosh function can also be calculated using complex exponential functions.
The complex inverse Cosh function can be represented by:
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arcos h(z) = log( z + √(z)2 - 1) |
Using the above equation we can add a new method to the "Complex class". (Note - Complex class is an integral part of our
software library and is not shown in these examples):
public static Complex Acosh(Complex c)
{
return log(c + Sqrt(c * c - 1.0));
}
Inverse Hyperbolic Tangent Function
The complex inverse Tanh function has the following relation:
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arctan h(z) = 1/2 [log(1 + z) - log(1 - z)] |
The following complex Tangent method is added to the Complex class:
public static Complex Atan(Complex c)
{
return 0.5 * [log(1 +c) - log(1 - c)];
}
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