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Results tagged with special-functions
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user 231922
Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.
0
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143
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Number of open tours by a biased rook on a specific $f(n)\times 1$ board which end on a $k$-...
We have a simple structure - biased rook of the two types.
Biased rook of the first kind which make open tours on a specific $f(n)\times 1$ board where $f(n) = \left\lfloor\log_2{2n}\right\rfloor + 1$ …
- 4,938
2
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90
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A subsequence expressed in terms of a sum with a triangle
We have a sequence which generalize A329369:
$$a(2n+1, p, q) = a(n, p,q), a(2n, p , q) = pa(n, p,q) + qa(n - 2^{f(n)}, p,q) + a(2n - 2^{f(n)}, p,q), a(0, p, q) = 1$$
where $f(n)$ is A007814, exponent …
- 4,938
1
vote
2
answers
501
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Recurrence for the sum
Let $m\geq 2$ be a fixed integer.
Let
$$f(n):=\begin{cases}
mf\left(\frac{n}{m}\right),&\text{if $n\mod m = 0$;}\\
1,&\text{otherwise}
\end{cases}$$
then if we have
$$a(n):=\begin{cases}
1,&\text{if $ …
- 4,938
1
vote
0
answers
91
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Recurrence for the viabin numbers of the self-conjugate integer partitions
Let $a(n)$ be A290254, the viabin numbers of the self-conjugate integer partitions, also defined as $\left\lbrace 0 \right\rbrace$ union fixed points of A059894, self-inverse permutation defined as fo …
- 4,938