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std::sinh(std::complex)

提供: cppreference.com
< cpp‎ | numeric‎ | complex
 
 
 
 
ヘッダ <complex> で定義
template< class T >
complex<T> sinh( const complex<T>& z );
(C++11およびそれ以降)

複素数の値 z の複素数の双曲線正弦を計算します。

目次

[編集] 引数

z - 複素数の値

[編集] 戻り値

エラーが発生しなければ、 z の複素数の双曲線正弦が返されます。

[編集] エラー処理と特殊な値

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

  • std::sinh(std::conj(z)) == std::conj(std::sinh(z))
  • std::sinh(z) == -std::sinh(-z)
  • If z is (+0,+0), the result is (+0,+0)
  • If z is (+0,+∞), the result is (±0,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
  • If z is (+0,NaN), the result is (±0,NaN)
  • If z is (x,+∞) (for any positive finite x), the result is (NaN,NaN) and FE_INVALID is raised
  • If z is (x,NaN) (for any positive finite x), the result is (NaN,NaN) and FE_INVALID may be raised
  • If z is (+∞,+0), the result is (+∞,+0)
  • If z is (+∞,y) (for any positive finite y), the result is +∞cis(y)
  • If z is (+∞,+∞), the result is (±∞,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
  • If z is (+∞,NaN), the result is (±∞,NaN) (the sign of the real part is unspecified)
  • If z is (NaN,+0), the result is (NaN,+0)
  • If z is (NaN,y) (for any finite nonzero y), the result is (NaN,NaN) and FE_INVALID may be raised
  • If z is (NaN,NaN), the result is (NaN,NaN)

where cis(y) is cos(y) + i sin(y)

[編集] ノート

双曲線正弦の数学的な定義は sinh z =
ez
-e-z
2
です。

双曲線正弦は複素平面上の整関数であり、分岐切断はありません。 双曲線正弦は虚部に関して 2πi の周期で周期的です。

[編集]

#include <iostream>
#include <cmath>
#include <complex>
 
int main()
{
    std::cout << std::fixed;
    std::complex<double> z(1, 0); // behaves like real sinh along the real line
    std::cout << "sinh" << z << " = " << std::sinh(z)
              << " (sinh(1) = " << std::sinh(1) << ")\n";
 
    std::complex<double> z2(0, 1); // behaves like sine along the imaginary line
    std::cout << "sinh" << z2 << " = " << std::sinh(z2)
              << " ( sin(1) = " << std::sin(1) << ")\n";
}

出力:

sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201)
sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471)

[編集] 関連項目

複素数の双曲線余弦 (ch(z)) を計算します
(関数テンプレート) [edit]
複素数の双曲線正接を計算します
(関数テンプレート) [edit]
複素数の逆双曲線正弦を計算します
(関数テンプレート) [edit]
双曲線正弦 (sh(x)) を計算します
(関数) [edit]
valarray の各要素に関数 std::sinh を適用します
(関数テンプレート) [edit]