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4
questions
5
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Determine whether or not $\exp\left(\sum_{n=1}^{\infty}\frac{B(n)}{n(n+1)}\right)$ is a rational number
Let $B(n)$ be the number of ones in the base 2 expression for the positive integer n.
Determine whether or not $$\exp\left(\sum_{n=1}^{\infty}\frac{B(n)}{n(n+1)}\right)$$ is a rational number.
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1
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0
answers
48
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Transforming a polynomial sum using a series expansion (BCH codes)
In my study of BCH codes I've come across the following equation (the "key equation"):
$$
\Omega(x) \equiv \Lambda(x)S(x) \mod x^{n-k} \tag{1}
$$
Where the two terms on the right are defined by:
$$
...
- 573
1
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1
answer
39
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What is $s_3$ and $s_4$ for $x$
$\sum_{i=0}^n i^k = s_k(n)$,
$s_k$ polynomial from degree $k+1$
I have already shown for $s_2(x) = \frac{x(x+1)(2x+1)}6$
How from the sum and $s_2(x)$ can be shown for $s_3(x)$ and $s_4(x)$ ...
1
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2
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What is the general formula for power series summation? [duplicate]
While reviewing definite integrals, $\int_a^bf(x)dx$; I recalled that a definite integral could not only be solved by the difference of the anti-derivatives of intervals b and a, $F(b)-F(a)$, via the ...
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