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- W2593403162 abstract "We prove two new forms of Jacobi-type J-fraction expansions generating the binomial coefficients, $binom{x+n}{n}$ and $binom{x}{n}$, over all $n geq 0$. Within the article we establish new forms of integer congruences for these binomial coefficient variations modulo any (prime or composite) $h geq 2$ and compare our results with existing known congruences for the binomial coefficients modulo primes $p$ and prime powers $p^k$. We also prove new exact formulas for these binomial coefficient cases from the expansions of the $h^{th}$ convergent functions to the infinite J-fraction series generating these coefficients for all $n$." @default.
- W2593403162 created "2017-03-16" @default.
- W2593403162 creator A5026138361 @default.
- W2593403162 date "2017-02-05" @default.
- W2593403162 modified "2023-09-27" @default.
- W2593403162 title "Jacobi-Type Continued Fractions and Congruences for Binomial Coefficients Modulo Integers $h geq 2$" @default.
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