本文以贝塞尔函数级数和的形式，给出了动态特性的理论解析解。

This paper gives a theoretical and analytical solution of the dynamic response for long gas pipeline in the form of infinite series with Bessel functions.

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重点是具有较大非线性的系统的方法，如FPK法，矩闭合法和函数级数法。

Emphasis is laid on the analysis, of large nonlinearities in system, for example, the FPK method, the closure method and the functional series expansion method.

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然后连续利用多元函数级数展开，导出群角表示的相速度和群速度近似公式。

Then series expansions of multi-variable functions are applied to the derived approximations in terms of phase angles to generate the approximations in terms of group angles.

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