Summary
We obtain bilinear sum rules for special functions of different kinds, namely first and second linearly independent solutions of a differential equation and with different arguments by means of the Green’s function technique. The sum rules obtained are a generalization of the Legendre sum rules.
Riassunto
In questo lavoro si utilizza il metodo della funzione di Green per dedurre nuove regole di somma per la funzione di Jacobi che è la generalizzazione della regola di somma delle funzioni di Legendre.
Резюме
Мы получаем билинейные пр вила сумм для специальных функций разного рода, например, для первых и вторых линейно независимых решений дифференциального уравнения и с различными аргументами с помощью техники функции Грина. Полученные правила сумм представляют обобщение правил сумм Лежандра.
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Capelas de Oliveira, E. New sum rules of special functions. Nuov Cim B 104, 701–707 (1989). https://doi.org/10.1007/BF02728459
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DOI: https://doi.org/10.1007/BF02728459