内维尔Θ函数 内维尔Θ函數Neville Theta functions共有四个定义如下 N e v i l l e C  z  m       q  m        k     q  m   k   k      c o s           k     π  z  K  m      K  m    m    displaystyle NevilleCzmfrac sqrt qmsum kinfty qmkkcoskpi zKmsqrt Kmm N e v i l l e T h e t a C  z  m      π   q  m        k     q  m  k   k     c o s           k     π  z  K  m      K  m    m    displaystyle NevilleThetaCzmfrac sqrt pi qmsum kinfty qmkkcoskpi zKmsqrt Kmm N e v i l l e T h e t a D  z  m          π          k     q  m   k    c o s  k  π  z  K  m       K  m   displaystyle NevilleThetaDzmfrac sqrt pi sum kinfty qmkcoskpi zKmsqrt Km N e v i l l e T h e t a N  z  m    π          k         k  q  m  k   c o s  k  π  z  K  m             m        K  m  displaystyle NevilleThetaNzmfrac sqrt pi sum kinfty kqmkcoskpi zKmsqrt msqrt Km displaystyle  其中 K  m   E l l i p t i c K   m   displaystyle KmEllipticKsqrt m K   m   E l l i p t i c K     m   displaystyle KmEllipticKsqrt m q  m   e  π  K  m  K   m  displaystyle qmefrac pi KmKm 尼维尔Θ函数也可以通过雅可比Θ函数的傅里叶级数来定义并使得尼维尔Θ函数可以进一步被用于定义相对应的雅可比椭圆函数 θ c  z  m    π q  m     m    K  m   k     q  m   k  k    cos     k    π z  K  m   displaystyle theta czmfrac sqrt pi qmmsqrt Kmsum kinfty qmkkcos leftfrac kpi zKmright θ d  z  m    π  K  m       k     q  m   k  cos   π z k K  m    displaystyle theta dzmfrac sqrt pi sqrt Kmleftsum kinfty qmkcos leftfrac pi zkKmrightright θ n  z  m    π     m     K  m       k        k  q  m   k  cos   π z k K  m    displaystyle theta nzmfrac sqrt pi msqrt Kmleftsum kinfty kqmkcos leftfrac pi zkKmrightright θ s  z  m    π q  m     m       m     K  m   k        k  q  m   k  k    sin     k    π z  K  m   displaystyle theta szmfrac sqrt pi qmmmsqrt Kmsum kinfty kqmkksin leftfrac kpi zKmright 这种定义涉及到第一类完全椭圆积分