Tanc函数

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Tanc 函数 定义如下[1]

Tanc(z)=tan(z)z
Tanc 2D plot
Tanc'(z) 2D plot
Tanc integral 2D plot
Tanc integral 3D plot
虚域虚部
  • Im(tan(x+iy)x+iy)
虚域实部
  • Re(tan(x+iy)x+iy)
绝对值
  • |tan(x+iy)x+iy|
一阶导数
  • 1tan(z))2ztan(z)z2
导数实部
  • Re(1(tan(x+iy))2x+iy+tan(x+iy)(x+iy)2)
导数虚部
  • Im(1(tan(x+iy))2x+iy+tan(x+iy)(x+iy)2)
导数绝对值
  • |1(tan(x+iy))2x+iy+tan(x+iy)(x+iy)2|

与其他特殊函数的关系

  • Tanc(z)=2iKummerM(1,2,2iz)(2z+π)KummerM(1,2,i(2z+π))
  • Tanc(z)=2i𝐻𝑒𝑢𝑛𝐵(2,0,0,0,2iz)(2z+π)𝐻𝑒𝑢𝑛𝐵(2,0,0,0,21/2i(2z+π))
  • Tanc(z)=WhittakerM(0,1/2,2iz)WhittakerM(0,1/2,i(2z+π))z

级数展开

Tancz(1+13z2+215z4+17315z6+622835z8+1382155925z10+218446081075z12+929569638512875z14+O(z16))

0ztan(x)xdx=(z+19z3+275z5+172205z7+6225515z9+13821715175z11+2184479053975z13+9295699577693125z15+O(z17))


图集

Tanc abs complex 3D
Tanc Im complex 3D plot
Tanc Re complex 3D plot
Tanc'(z) Im complex 3D plot
Tanc'(z) Re complex 3D plot
Tanc'(z) abs complex 3D plot
Tanc abs plot
Tanc Im plot
Tanc Re plot
Tanc'(z) Im plot
Tanc'(z) abs plot
Tanc'(z) Re plot
Tanc integral abs plot
Tanc integral Im plot
Tanc integral Re plot
Tanc abs complex 3D plot
Tanc Im complex 3D plot
Tanc Re complex 3D plot

参看

参考文献

  1. Weisstein, Eric W. "Tanc Function." From MathWorld--A Wolfram Web Resource. -{R|http://mathworld.wolfram.com/TancFunction.html}- Template:Wayback