From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fcasinh.html | 77 +++++++++++++++++++++++++++++++ 1 file changed, 77 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcasinh.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcasinh.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcasinh.html b/devdocs/c/numeric%2Fcomplex%2Fcasinh.html new file mode 100644 index 00000000..9ef02d9c --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcasinh.html @@ -0,0 +1,77 @@ +

casinhf, casinh, casinhl

Defined in header <complex.h> 
float complex       casinhf( float complex z );
+		 (1) (since C99) 
double complex      casinh( double complex z );
+		 (2) (since C99) 
long double complex casinhl( long double complex z );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define asinh( z )
+		 (4) (since C99)
+1-3) Computes the complex arc hyperbolic sine of z with branch cuts outside the interval [−i; +i] along the imaginary axis.
+4) Type-generic macro: If z has type long double complex, casinhl is called. if z has type double complex, casinh is called, if z has type float complex, casinhf is called. If z is real or integer, then the macro invokes the corresponding real function (asinhf, asinh, asinhl). If z is imaginary, then the macro invokes the corresponding real version of the function asin, implementing the formula asinh(iy) = i asin(y), and the return type is imaginary.

Parameters

+ +
z - complex argument

Return value

If no errors occur, the complex arc hyperbolic sine of z is returned, in the range of a strip mathematically unbounded along the real axis and in the interval [−iπ/2; +iπ/2] along the imaginary axis.

+

Error handling and special values

Errors are reported consistent with math_errhandling

+

If the implementation supports IEEE floating-point arithmetic,

+

Notes

Although the C standard names this function "complex arc hyperbolic sine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "complex inverse hyperbolic sine", and, less common, "complex area hyperbolic sine".

+

Inverse hyperbolic sine is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-i∞,-i) and (i,i∞) of the imaginary axis.

+

The mathematical definition of the principal value of the inverse hyperbolic sine is asinh z = ln(z + √1+z2) For any z, asinh(z) =

+asin(iz)/i

Example

#include <stdio.h>
+#include <complex.h>
+ 
+int main(void)
+{
+    double complex z = casinh(0+2*I);
+    printf("casinh(+0+2i) = %f%+fi\n", creal(z), cimag(z));
+ 
+    double complex z2 = casinh(-conj(2*I)); // or casinh(CMPLX(-0.0, 2)) in C11
+    printf("casinh(-0+2i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
+ 
+    // for any z, asinh(z) = asin(iz)/i
+    double complex z3 = casinh(1+2*I);
+    printf("casinh(1+2i) = %f%+fi\n", creal(z3), cimag(z3));
+    double complex z4 = casin((1+2*I)*I)/I;
+    printf("casin(i * (1+2i))/i = %f%+fi\n", creal(z4), cimag(z4));
+}

Output:

+
casinh(+0+2i) = 1.316958+1.570796i
+casinh(-0+2i) (the other side of the cut) = -1.316958+1.570796i
+casinh(1+2i) = 1.469352+1.063440i
+casin(i * (1+2i))/i =  1.469352+1.063440i

References

See also

+ + + + +
+
(C99)(C99)(C99)
 computes the complex arc hyperbolic cosine
(function)
+
(C99)(C99)(C99)
 computes the complex arc hyperbolic tangent
(function)
+
(C99)(C99)(C99)
 computes the complex hyperbolic sine
(function)
+
(C99)(C99)(C99)
 computes inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x))
(function)
C++ documentation for asinh
+

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Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/complex/casinh +

+
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