Coshc函数维基百科,自由的 encyclopedia Coshc函数常见于有关光学散射[1]、海森堡时空[2]和双曲几何学的论文中[3]其定义如下:[4][5] Coshc ( z ) = cosh ( z ) z {\displaystyle \operatorname {Coshc} (z)={\frac {\cosh(z)}{z}}} 它是下列微分方程的一个解: w ( z ) z − 2 d d z w ( z ) − z d 2 d z 2 w ( z ) = 0 {\displaystyle w\left(z\right)z-2\,{\frac {d}{dz}}w\left(z\right)-z{\frac {d^{2}}{d{z}^{2}}}w\left(z\right)=0} Coshc 2D plot Coshc'(z) 2D plot 复域虚部 Im ( cosh ( x + i y ) x + i y ) {\displaystyle \operatorname {Im} \left({\frac {\cosh(x+iy)}{x+iy}}\right)} 复域实部 Re ( cosh ( x + i y ) x + i y ) {\displaystyle \operatorname {Re} \left({\frac {\cosh \left(x+iy\right)}{x+iy}}\right)} 绝对值 | cosh ( x + i y ) x + i y | {\displaystyle \left|{\frac {\cosh(x+iy)}{x+iy}}\right|} 一阶导数 sinh ( z ) z − cosh ( z ) z 2 {\displaystyle {\frac {\sinh(z)}{z}}-{\frac {\cosh(z)}{z^{2}}}} 导数实部 − Re ( − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 ) {\displaystyle -\operatorname {Re} \left(-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right)} 导数虚部 − Im ( − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 ) {\displaystyle -\operatorname {Im} \left(-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right)} 导数绝对值 | − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 | {\displaystyle \left|-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right|}
Coshc函数常见于有关光学散射[1]、海森堡时空[2]和双曲几何学的论文中[3]其定义如下:[4][5] Coshc ( z ) = cosh ( z ) z {\displaystyle \operatorname {Coshc} (z)={\frac {\cosh(z)}{z}}} 它是下列微分方程的一个解: w ( z ) z − 2 d d z w ( z ) − z d 2 d z 2 w ( z ) = 0 {\displaystyle w\left(z\right)z-2\,{\frac {d}{dz}}w\left(z\right)-z{\frac {d^{2}}{d{z}^{2}}}w\left(z\right)=0} Coshc 2D plot Coshc'(z) 2D plot 复域虚部 Im ( cosh ( x + i y ) x + i y ) {\displaystyle \operatorname {Im} \left({\frac {\cosh(x+iy)}{x+iy}}\right)} 复域实部 Re ( cosh ( x + i y ) x + i y ) {\displaystyle \operatorname {Re} \left({\frac {\cosh \left(x+iy\right)}{x+iy}}\right)} 绝对值 | cosh ( x + i y ) x + i y | {\displaystyle \left|{\frac {\cosh(x+iy)}{x+iy}}\right|} 一阶导数 sinh ( z ) z − cosh ( z ) z 2 {\displaystyle {\frac {\sinh(z)}{z}}-{\frac {\cosh(z)}{z^{2}}}} 导数实部 − Re ( − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 ) {\displaystyle -\operatorname {Re} \left(-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right)} 导数虚部 − Im ( − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 ) {\displaystyle -\operatorname {Im} \left(-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right)} 导数绝对值 | − 1 − ( cosh ( x + i y ) ) 2 x + i y + cosh ( x + i y ) ( x + i y ) 2 | {\displaystyle \left|-{\frac {1-(\cosh(x+iy))^{2}}{x+iy}}+{\frac {\cosh(x+iy)}{(x+iy)^{2}}}\right|}