Abstract We prove some trigonometric identities involving Chebyshev polynomials of the second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factor calculations for highly excited states.

中文翻译：

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受原子形状因子启发的三角恒等式

摘要 我们证明了一些涉及第二类切比雪夫多项式的三角恒等式。身份的灵感来自原子形状因子计算。如果发现这些恒等式的概括，将有助于提高高激发态的原子形状因子计算的数值稳定性。