Bernoulli and Euler Polynomials - 24.19 Methods of Computation
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 24.19#Ex2 | \BernoullinumberB{2n} = \dfrac{N_{2n}}{D_{2n}} |
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bernoulli(2*n) = (N[2*n])/(D[2*n])
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BernoulliB[2*n] == Divide[Subscript[N, 2*n],Subscript[D, 2*n]]
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Failure | Failure | Failed [300 / 300] Result: -.8333333333
Test Values: {D[2*n] = 1/2*3^(1/2)+1/2*I, N[2*n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: -1.033333333
Test Values: {D[2*n] = 1/2*3^(1/2)+1/2*I, N[2*n] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: -0.8333333333333334
Test Values: {Rule[n, 1], Rule[Subscript[D, Times[2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[N, Times[2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: -1.0333333333333334
Test Values: {Rule[n, 2], Rule[Subscript[D, Times[2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[N, Times[2, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 24.19.E3 | \frac{t^{2}}{\cosh@@{t}-1} = -2\sum_{n=0}^{\infty}(2n-1)\BernoullinumberB{2n}\frac{t^{2n}}{(2n)!} |
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((t)^(2))/(cosh(t)- 1) = - 2*sum((2*n - 1)*bernoulli(2*n)*((t)^(2*n))/(factorial(2*n)), n = 0..infinity)
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Divide[(t)^(2),Cosh[t]- 1] == - 2*Sum[(2*n - 1)*BernoulliB[2*n]*Divide[(t)^(2*n),(2*n)!], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Successful [Tested: 6] | Skipped - Because timed out |