关于Volterra方程的级数解
On series solutions of Volterra equations
摘要：
我们推导出计算Volterra积分方程系统解的泰勒系数的公式，包括线性和非线性的，无论是没有奇异性还是具有Abel型和对数型奇异性。我们还获得了某些系统的第一类Volterra方程的解决方案。在所有情况下，除了对数奇点的情况下，我们得到的泰勒系数的计算递归公式。在某些情况下，我们给出了收敛性的证明和严格的估计的收敛半径。
英文摘要：
We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive formulae for the calculation of the Taylor coefficients. In certain cases, we give proofs of convergence and rigorous estimates of the radius of convergence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
