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Properties of the zeros of the classical polynomials and of the Bbessel functions

Свойства нулей классических полиномов и бесселевых функций

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

Many algebraic equations satisfied by the zeros of the classical polynomials and of the Bessel functions are reported. Some of them are collected from recent papers; several of them are new; most of them display remarkable diophantine features. Certain matrices constructed with arbitrary numbers rather than the zeros of special functions, but displaying analogous diophantine properties, are also exhibited.

Riassunto

Si riportano molte equazioni algebriche soddisfatte dagli zeri dei polinomi classici e delle funzioni di Bessel. Alcune sono riprese da lavori recenti; numerose sono nuove; la maggioranza esibisce notevoli proprietà di carattere diofantino. Si esibiscono inoltre alcune matrici, costruite con numeri arbitrari anziché con gli zeri di funzioni speciali, che anche loro posseggono però delle notevoli proprietà diofantine.

Резюме

Приводится большое число алгебраических уравнений, которым удовлетворяют нули классических полиномов и бесселевых функций. Некоторые из уравнений взяты из недавних работ, некоторые из них новые. Большинство из них обнаруживают интересные особенности. Указываются некоторые матрицы, сконструированные с помощью произвольного числа нулей специальных функций.

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References

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Authors and Affiliations

  1. Istituto di Fisica dell’Università, 00185, Roma

    S. Ahmed, M. Bruschi & F. Calogero

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Roma, Italy

    S. Ahmed, M. Bruschi & F. Calogero

  3. Institute of Theoretical and Experimental Physics, Moscow

    M. A. Olshanetsky & A. M. Perelomov

Authors
  1. S. Ahmed
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  2. M. Bruschi
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  3. F. Calogero
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  4. M. A. Olshanetsky
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  5. A. M. Perelomov
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Ahmed, S., Bruschi, M., Calogero, F. et al. Properties of the zeros of the classical polynomials and of the Bbessel functions. Nuov Cim B 49, 173–199 (1979). https://doi.org/10.1007/BF02737517

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