Bernoulli polynomials
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1: 24.1 Special Notation
2: 24.3 Graphs
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3: 24.16 Generalizations
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►For , Bernoulli and Euler polynomials of order
are defined respectively by
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►For extensions of to complex values of , , and , and also for uniform asymptotic expansions for large and large , see Temme (1995b) and López and Temme (1999b, 2010b).
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24.16.6
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is a polynomial in of degree .
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4: 24.4 Basic Properties
5: 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)). …6: 25.1 Special Notation
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nonnegative integers. | |
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Bernoulli number and polynomial (§24.2(i)). | |
periodic Bernoulli function . | |
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7: 24.13 Integrals
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§24.13(i) Bernoulli Polynomials
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24.13.1
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24.13.6
►For integrals of the form and see Agoh and Dilcher (2011).
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§24.13(iii) Compendia
…8: 24.21 Software
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