Power series for inverse Jacobian elliptic functions
Power series for inverse Jacobian elliptic functions
复制标题
逆雅可比椭圆函数的幂级数
DOI：
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发表时间：
2008
影响因子：
2
通讯作者：
B. C. Carlson
中科院分区：
文献类型：
--
作者：
B. C. Carlson
利用第一类对称椭圆积分的性质，将12个雅可比逆椭圆函数展开为幂级数。合适的符号允许三个系列包括所有12种情况，其中三种已经给出。所有系数都是模数为k的多项式它们是勒让德多项式的齐次变体。三个子集中的每一个序列都有相同的以k表示的系数。
The 12 inverse Jacobian elliptic functions are expanded in power series by using properties of the symmetric elliptic integral of the first kind. Suitable notation allows three series to include all 12 cases, three of which have been given previously. All coefficients are polynomials in the modulus k that are homogeneous variants of Legendre polynomials. The four series in each of three subsets have the same coefficients in terms of k.