椭圆周上的一类新的双正交级数

A KIND OF NEW BIORTHOGONAL SERIES ON AN ELLIPSE

研究了椭圆周上一类新的双正交级数，给出了它的部分和与其诱导函数的Ｆｏｕｒｉｅｒ三角级数的部分和之间偏差的精确的渐近表达式．

By ωn (z),Hn(z) denote mixed Jacobi polynomial(α,β )and the corresponding function of second kind.Let Gd be an ellipse: z=ch(τ+ iθ) (0 ≤θ≤2π), eτ=d. On Gd the series∑ (fnωn(z) + f-nHn(z) ) is discussed, where f ∈L (Gd) ; fn,Between the above series and the Fourier trigonometric series of f(ch (τ+ iθ) ), an equiconvergence theorem is given.