In this paper, we consider and obtain binomial sums and alternating binomial
sums including falling factorial of the summation indices. For example, for
nonnegative integer $m,$
\begin{eqnarray*}
&&\sum\limits_{k=0}^{n}\dbinom{n}{k}k^{\underline{m}}U_{2k}^{2m}=\frac{n^{\underline{m}}}{\left( p^{2}+4\right) ^{m}}\left(
\sum\limits_{i=0}^{m}\left( -1\right) ^{i}\dbinom{2m}{i}V_{2\left(
m-i\right) }^{n-m}V_{2\left( m+n\right) \left( m-i\right) }-\left( -1\right)
^{m}2^{n-m}\dbinom{2m}{m}\right),
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 15 Ekim 2020 |
Gönderilme Tarihi | 23 Mart 2020 |
Kabul Tarihi | 5 Mayıs 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 8 Sayı: 2 |
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