little q-Jacobi polynomials
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21: 24.18 Physical Applications
§24.18 Physical Applications
►Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). ►Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).22: 3.2 Linear Algebra
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►When the factorization (3.2.5) is available, the accuracy of the computed solution can be improved with little extra computation.
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►The polynomial
…The multiplicity of an eigenvalue is its multiplicity as a zero of the characteristic polynomial (§3.8(i)).
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►Its characteristic polynomial can be obtained from the recursion
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23: Bibliography D
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Computing Riemann matrices of algebraic curves.
Phys. D 152/153, pp. 28–46.
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On the real roots of Euler polynomials.
Monatsh. Math. 106 (2), pp. 115–138.
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On multiple zeros of Bernoulli polynomials.
Acta Arith. 134 (2), pp. 149–155.
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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets.
SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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24: 27.16 Cryptography
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►Procedures for finding such primes require very little computer time.
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