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21: 24.14 Sums
§24.14 Sums
►§24.14(i) Quadratic Recurrence Relations
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24.14.6
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§24.14(ii) Higher-Order Recurrence Relations
… ►For other sums involving Bernoulli and Euler numbers and polynomials see Hansen (1975, pp. 331–347) and Prudnikov et al. (1990, pp. 383–386).22: 27.9 Quadratic Characters
§27.9 Quadratic Characters
►For an odd prime , the Legendre symbol is defined as follows. … ►
27.9.2
►If are distinct odd primes, then the quadratic reciprocity law states that
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►If an odd integer has prime factorization , then the Jacobi symbol
is defined by , with .
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23: 24.5 Recurrence Relations
§24.5 Recurrence Relations
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24.5.4
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24.5.5
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§24.5(ii) Other Identities
… ►§24.5(iii) Inversion Formulas
…24: Bibliography
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Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
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Sharp bounds for the Bernoulli numbers.
Arch. Math. (Basel) 74 (3), pp. 207–211.
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Number Theory.
In The New Encyclopaedia Britannica,
Vol. 25, pp. 14–37.
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A Centennial History of the Prime Number Theorem.
In Number Theory,
Trends Math., pp. 1–14.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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25: 24.2 Definitions and Generating Functions
§24.2 Definitions and Generating Functions
►§24.2(i) Bernoulli Numbers and Polynomials
… ►§24.2(ii) Euler Numbers and Polynomials
… ► … ► …26: 24.6 Explicit Formulas
27: 27.5 Inversion Formulas
§27.5 Inversion Formulas
… ►Generating functions yield many relations connecting number-theoretic functions. … ►Special cases of Möbius inversion pairs are: … ►Other types of Möbius inversion formulas include: … ►28: Bibliography T
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New congruences for the Bernoulli numbers.
Math. Comp. 48 (177), pp. 341–350.
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Asymptotic estimates of Stirling numbers.
Stud. Appl. Math. 89 (3), pp. 233–243.
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Explicit formulas for the Bernoulli and Euler polynomials and numbers.
Abh. Math. Sem. Univ. Hamburg 61, pp. 175–180.
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On the theory of the Bernoulli polynomials and numbers.
J. Math. Anal. Appl. 104 (2), pp. 309–350.
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Theory of the Fresnel integral.
USSR Comput. Math. and Math. Phys. 9 (4), pp. 271–279.
29: 24.21 Software
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