On the recursive sequence xn+1=xn−4k+31+∏t=02xn−k+1t−k$$ {x}_{n+1}=\frac{x_{n-\left(4k+3\right)}}{1+\prod_{t=0}^2{x}_{n-\left(k+1\right)t-k}} $$
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DOI: 10.1007/s10958-017-3330-7
Abstract: AbstractThe solution of the difference equationxn+1=xn−4k+31+∏t=02xn−k+1t−k,n=0,1,2,…,$$ {x}_{n+1}=\frac{x_{n-\left(4k+3\right)}}{1+\prod_{t=0}^2{x}_{n-\left(k+1\right)t-k}},\kern0.5em n=0,1,2,\dots, $$ where x−(4k+3), x−(4k+2), . . . , x−1, x0 ∈ (0, ∞) and k = 0, 1, . . . , is studied. read more here.
Keywords: left right; prod left; 02xn frac; frac left ... See more keywords
On the Recursive Sequence xn+1=xn−k+11+xnxn−1…xn−k$$ {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}} $$
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DOI: 10.1007/s10958-018-3982-y
Abstract: A solution of the following difference equation is investigated:xn+1=xn−k+11+xnxn−1…xn−k,n=0,1,2,…$$ {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}},n=0,1,2,\dots $$where x−(k+1); x−k; : : : ; x−1; x0 ???? (0;∞) and k = 0; 1; 2; : : : . read more here.
Keywords: left right; right dots; recursive sequence; frac left ... See more keywords