^PN Den Outer, TM Nieuwenhuizen, A Lagendijk,Location of objects in multiple-scattering media,JOSA A, Vol. 10, Issue 6, pp. 1209-1218 (1993)
^T Körpinar ,New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime - International Journal of Theoretical Physics, 2014 - Springer
^Nilg¨un S¨onmez,A Trigonometric Proof of the Euler Theorem in Hyperbolic Geometry,International Mathematical Forum, 4, 2009, no. 38, 1877 - 1881
^JHM ten Thije Boonkkamp, J van Dijk, L Liu,Extension of the complete flux scheme to systems of conservation laws,J Sci Comput (2012) 53:552–568,DOI 10.1007/s10915-012-9588-5
coshc函数, 常见于有关光学散射, 海森堡时空, 和双曲几何学的论文中, 其定义如下, coshc, cosh, displaystyle, operatorname, coshc, frac, cosh, 它是下列微分方程的一个解, displaystyle, left, right, frac, left, right, frac, left, right, coshc, plotcoshc, plot复域虚部im, cosh, displaystyle, operatorname, left, frac,. 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 plotCoshc 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 目录 1 表示为其他特殊函数 2 级数展开 3 图集 4 参见 5 参考文献表示为其他特殊函数 编辑Coshc z i z 1 2 p M 1 2 i p 2 z e 1 2 i p z z displaystyle operatorname Coshc z frac left iz 1 2 pi right rm M left 1 2 i pi 2 z right rm e 1 2 i pi z z nbsp Coshc z 1 2 2 i z p H e u n B 2 0 0 0 2 1 2 i p z e 1 2 i p z z displaystyle operatorname Coshc z frac 1 2 frac left 2 iz pi right it HeunB left 2 0 0 0 sqrt 2 sqrt 1 2 i pi z right rm e 1 2 i pi z z nbsp Coshc z i 2 i z p W h i t t a k e r M 0 1 2 i p 2 z 4 i z 2 p z displaystyle operatorname Coshc z frac i left 2 iz pi right rm mathbf W hittakerM left 0 1 2 i pi 2 z right left 4 iz 2 pi right z nbsp 级数展开 编辑Coshc z z 1 1 2 z 1 24 z 3 1 720 z 5 1 40320 z 7 1 3628800 z 9 1 479001600 z 11 1 87178291200 z 13 O z 15 displaystyle operatorname Coshc z approx z 1 frac 1 2 z frac 1 24 z 3 frac 1 720 z 5 frac 1 40320 z 7 frac 1 3628800 z 9 frac 1 479001600 z 11 frac 1 87178291200 z 13 O left z 15 right nbsp 图集 编辑 nbsp Coshc abs complex 3D nbsp Coshc Im complex 3D plot nbsp Coshc Re complex 3D plot nbsp Coshc z Im complex 3D plot nbsp Coshc z Re complex 3D plot nbsp Coshc z abs complex 3D plot nbsp Coshc x abs density plot nbsp Coshc x Im density plot nbsp Coshc x Re density plot参见 编辑Tanc函数 Tanhc函数 Sinhc函数参考文献 编辑 PN Den Outer TM Nieuwenhuizen A Lagendijk Location of objects in multiple scattering media JOSA A Vol 10 Issue 6 pp 1209 1218 1993 T Korpinar New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime International Journal of Theoretical Physics 2014 Springer Nilg un S onmez A Trigonometric Proof of the Euler Theorem in Hyperbolic Geometry International Mathematical Forum 4 2009 no 38 1877 1881 JHM ten Thije Boonkkamp J van Dijk L Liu Extension of the complete flux scheme to systems of conservation laws J Sci Comput 2012 53 552 568 DOI 10 1007 s10915 012 9588 5 Weisstein Eric W Coshc Function From MathWorld A Wolfram Web Resource http mathworld wolfram com CoshcFunction html 永久失效連結 取自 https zh wikipedia org w index php title Coshc函数 amp oldid 57892675, 维基百科,wiki,书籍,书籍,图书馆,