地平面上方垂直磁流元电磁场的精确解析表达式

摘要

利用倍特曼(Bateman)展开公式，地平面上方垂直磁流元电磁场中的索末菲型积分被表达成快速、绝对收敛的球面波展开式；应用超几何函数的巴恩斯(Barnes)积分表达式，展开系数被表达成以复介电常数为宗量的雅可比多项式。该展开式是此类索末菲半空间问题精确解答，它能够为相关电磁场问题研究提供方便、准确的解析表达式。%By using the Bateman's expansion formula, Sommerfeld typeintegral contained in electromagnetic fields of a vertical magnetic current element over the ground plane is expressed as a rapidly and absolutely convergent series of spherical wave functions, and the coefficients of the series are cast into the Jacobi polynomials for the complex permittivity by the aid of the Barne's integral representation of the hypergeometric function. The obtained result is an accurate and analytical expression for the Sommerfeld half-space problem and can give a good service to correlated investigations in theory of electromagnetic fields.