求勒让德函数零点的两个展开式

TWO EXPANSIONS SUITABLE FOR COMPUTING THE ZEROS OF LEGENDRE FUNCTIONS

利用勒让德函数在θ≈π时的恰当展开式,本文给出了(P_(V_n))~1(cosθ)及d/dθ(P_(V_n))~1(cosθ)零点的数值解。当θ=165°时,本文结果与文献[1]、[2]中给出的数值结果吻合极好。当θ=175°、177°、179°时,本文还给出了前17个零点的值。

Using the appropriate series expansion for the Legendre functions valid for θ≈π,the zeros of P_(vn)~1 (cosθ)and d/dθP_(μn)~1(cosθ)are computed numerically.For θ=165°, the results computed here are in good agreement with those given by Ref.[1～2]. The first seventeenth zeros are also given in this paper forθ=175°, 177° and 179°.