Bogart Other Mul 根式函数= a的多值性 采用极坐标表达式=peo,z-a=re 代入则有 T p=+nrn=0,±1,±2,… 因此,对于给定的一个值,有两个值与 对应
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼êw = √ z − aõ5 æ^4ILªw = ρe iφ , z − a = re iθ \Kk ρ = √ r φ = θ 2 + nπ n = 0, ±1, ±2, · · · Ïd§éu½z§küw éAµ w1(z) =√ re iθ/2 un = 0, ±2, · · · w2(z) =√ re i(π+θ/2) = − √ re iθ/2 un = ±1, ±3, · · · C. S. Wu 1nù õ¼ê
Bogart Other Mul 根式函数= a的多值性 采用极坐标表达式=peo,z-a=re 代入则有 、/T 2+nxm=0,1,+2 因此,对于给定的一个z值,有两个值与之 对应: 1(2)=yr 2 相当于n=0,±2, u2(2) i(+6/2) √e2相当于n=士1+3(索
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions ª¼êw = √ z − aõ5 æ^4ILªw = ρe iφ , z − a = re iθ \Kk ρ = √ r φ = θ 2 + nπ n = 0, ±1, ±2, · · · Ïd§éu½z§küw éAµ w1(z) =√ re iθ/2 un = 0, ±2, · · · w2(z) =√ re i(π+θ/2) = − √ re iθ/2 un = ±1, ±3, · · · C. S. Wu 1nù õ¼ê
Other ugarit 结论 根式函数=√z-a的多值性 ρ多值性来源于辐角的多值性 准确说,多值性来源于宗量-a(而非自变 量2)辐角的多值性 多值性的表现则是函数的辐角
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions (Ø ª¼êw = √ z − aõ5 õ55 uËõ5 O(`§õ55 umþz − a( gC þz)Ëõ5 õ5LyK´¼êwË (½å§±Òr¼êw = √ z − a²(L «¤ |w| = p |z − a| arg w = 1 2 arg(z − a) C. S. Wu 1nù õ¼ê
Other ugarit 结论 根式函数=√z-a的多值性 多值性来源于辐角的多值性 准确说,多值性来源于宗量z-α(而非自变 量z)辐角的多值性 多值性的表现则是函数的辐角
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions (Ø ª¼êw = √ z − aõ5 õ55 uËõ5 O(`§õ55 umþz − a( gC þz)Ëõ5 õ5LyK´¼êwË (½å§±Òr¼êw = √ z − a²(L «¤ |w| = p |z − a| arg w = 1 2 arg(z − a) C. S. Wu 1nù õ¼ê
Other ugarit 结论 根式函数=√z-a的多值性 多值性来源于辐角的多值性 准确说,多值性来源于宗量z-α(而非自变 量z)辐角的多值性 多值性的表现则是函数v的辐角
Root Functions Logarithmic Functions Other Multivalued Functions Multivalued Property of Root Functions Branching Points in Root Functions Branch Cut of Root Functions Riemann Surface of Root Functions (Ø ª¼êw = √ z − aõ5 õ55 uËõ5 O(`§õ55 umþz − a( gC þz)Ëõ5 õ5LyK´¼êwË (½å§±Òr¼êw = √ z − a²(L «¤ |w| = p |z − a| arg w = 1 2 arg(z − a) C. S. Wu 1nù õ¼ê