Question

$\sum_{i=0}^{S/2} (S/2+3/2)^{2i}\frac{2\cdot\Gamma(a) \Gamma(i+0.5)}{\sqrt(\pi) \Gamma(a+i+1)} {S \choose 2i} B_{\frac{S-2i}{2}}^{1+S}(0.5+S/2) $

score 29 · Answer 1 · 2019-02-21 09:41:11

$\sum_{i=0}^{S/2} (S/2+3/2)^{2i}\frac{2\cdot\Gamma(a) \Gamma(i+0.5)}{\sqrt(\pi) \Gamma(a+i+1)} {S \choose 2i} B_{\frac{S-2i}{2}}^{1+S}(0.5+S/2) $

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score 104 · Answer 12 · 2019-10-22 13:43:38

104

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List Question

$\sum_{i=0}^{S/2} (S/2+3/2)^{2i}\frac{2\cdot\Gamma(a) \Gamma(i+0.5)}{\sqrt(\pi) \Gamma(a+i+1)} {S \choose 2i} B_{\frac{S-2i}{2}}^{1+S}(0.5+S/2) $

When solving differential equations using substitution, does it really matter which substitution you choose?

Property of the Bernoulli Polynomials

Is there a polynomial (or series) expression for summing $S_d(a,N)=\sum_{k=0}^{N-1} \log(1+{1\over a+k \cdot d})$? (perhaps Bernoulli-type)

Property of the remainder term in the Euler-Maclaurin formula for $\sum_{i=1}^n\log i$.

Integrating periodic Bernoulli function

Periodic Bernoulli polynomials

Bernoulli Substitution for differential equation

Identity of Bernoulli polynomials

Sum with Bernoulli polynomial

How to describe $\overset{\sim}{B}_n(x):=\sum_{k=0}^n\binom{n}{k}B^-_{n-k}H_kx^k$ and in particular $\overset{\sim}{B}_n(1)$?

How to associate Bernouli numbers or Bernouli polynomials into the relation $ \sum_{n=0}^{\infty} \left[n(4x-1)+(2x) \right]x^n=0$?

Can we write $B_n(x)-B_n(0)=nx^{n-1}$?

The Bernoulli Polynomials

integral representation for $\sum_{k=0}^{x}k^{p}$

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