csinhf, csinh, csinhl
From cppreference.com
Defined in header
<complex.h>
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(1) | (since C99) | |
(2) | (since C99) | |
(3) | (since C99) | |
Defined in header
<tgmath.h>
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#define sinh( z )
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(4) | (since C99) |
1-3) Computes the complex hyperbolic sine of
z
.
4) Type-generic macro: If
z
has type long double complex, csinhl
is called. if z
has type double complex, csinh
is called, if z
has type float complex, csinhf
is called. If z
is real or integer, then the macro invokes the corresponding real function (sinhf, sinh, sinhl). If z
is imaginary, then the macro invokes the corresponding real version of the function sin, implementing the formula sinh(iy) = i sin(y), and the return type is imaginary.
Contents |
[edit] Parameters
z | - | complex argument |
[edit] Return value
If no errors occur, complex hyperbolic sine of z
is returned
[edit] Error handling and special values
Errors are reported consistent with math_errhandling
If the implementation supports IEEE floating-point arithmetic,
- csinh(conj(z)) == conj(csinh(z))
- csinh(z) == -csinh(-z)
- If
z
is+0+0i
, the result is+0+0i
- If
z
is+0+∞i
, the result is±0+NaNi
(the sign of the real part is unspecified) and FE_INVALID is raised - If
z
is+0+NaNi
, the result is±0+NaNi
- If
z
isx+∞i
(for any positive finite x), the result isNaN+NaNi
and FE_INVALID is raised - If
z
isx+NaNi
(for any positive finite x), the result isNaN+NaNi
and FE_INVALID may be raised - If
z
is+∞+0i
, the result is+∞+0i
- If
z
is+∞+yi
(for any positive finite y), the result is+∞+cis(y)
- If
z
is+∞+∞i
, the result is±∞+NaNi
(the sign of the real part is unspecified) and FE_INVALID is raised - If
z
is+∞+NaNi
, the result is±∞+NaNi
(the sign of the real part is unspecified) - If
z
isNaN+0i
, the result isNaN+0i
- If
z
isNaN+yi
(for any finite nonzero y), the result isNaN+NaNi
and FE_INVALID may be raised - If
z
isNaN+NaNi
, the result isNaN+NaNi
where cis(y) is cos(y) + i sin(y)
[edit] Notes
Mathematical definition of hyperbolic sine is sinh z =ez -e-z |
2 |
Hyperbolic sine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi
[edit] Example
Run this code
#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = csinh(1); // behaves like real sinh along the real line printf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n", creal(z), cimag(z), sinh(1)); double complex z2 = csinh(I); // behaves like sine along the imaginary line printf("sinh(0+1i) = %f%+fi ( sin(1)=%f)\n", creal(z2), cimag(z2), sin(1)); }
Output:
sinh(1+0i) = 1.175201+0.000000i (sinh(1)=1.175201) sinh(0+1i) = 0.000000+0.841471i ( sin(1)=0.841471)
[edit] References
- C11 standard (ISO/IEC 9899:2011):
-
- 7.3.6.5 The csinh functions (p: 194)
-
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
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- G.6.2.5 The csinh functions (p: 541-542)
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- G.7 Type-generic math <tgmath.h> (p: 545)
- C99 standard (ISO/IEC 9899:1999):
-
- 7.3.6.5 The csinh functions (p: 175-176)
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- 7.22 Type-generic math <tgmath.h> (p: 335-337)
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- G.6.2.5 The csinh functions (p: 476-477)
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- G.7 Type-generic math <tgmath.h> (p: 480)
[edit] See also
(C99)(C99)(C99)
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computes the complex hyperbolic cosine (function) |
(C99)(C99)(C99)
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computes the complex hyperbolic tangent (function) |
(C99)(C99)(C99)
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computes the complex arc hyperbolic sine (function) |
(C99)(C99)
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computes hyperbolic sine (sh(x)) (function) |
C++ documentation for sinh
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