An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow and the loss of significant figures. A rigorous and closed form solution of the integral is derived in this paper based on the recurrence method, which is accurate in the whole frequency range and thousands of times faster than the existing methods. It is shown that the proposed method can be extended for the calculation of the sound radiated by a baffled piston and an unbaffled resilient disk with axisymmetric velocity and pressure profiles, respectively, and some baffled rotating sources where the velocity profile is asymmetric.

中文翻译：

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关于计算带挡板的圆形活塞辐射声的球面展开

计算带挡板的圆形刚性活塞辐射的声音的一种有效且准确的方法是使用球谐函数，其解是包含球面贝塞尔函数积分的级数。现有文献中积分通常采用广义超几何函数计算，由于溢出和有效数字丢失，在中高频处收敛性较差。本文基于递推法推导了积分的严格闭式解，在整个频率范围内准确，比现有方法快数千倍。结果表明，所提出的方法可以扩展用于计算由具有轴对称速度和压力分布的挡板活塞和无挡板弹性盘辐射的声音，