Polynomials calculating sums of powers of arithmetic progressions (Q111954161)
Jump to navigation
Jump to search
Vector of polynomials calculating sums of terms with addends with bases in arithmetic progression and non-negative integer exponents
- Pietrocola's formula
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomials calculating sums of powers of arithmetic progressions |
Vector of polynomials calculating sums of terms with addends with bases in arithmetic progression and non-negative integer exponents |
|
Statements
![{\displaystyle {[A]_{r,c}}={\begin{cases}0,&{\text{if }}c>r,\\{\dbinom {r}{c-1}},&{\text{if }}c\leq r,\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39297f9edb9f96d09e0d11c3d3ff42951669905d)
![{\displaystyle [T(h,d)]_{r,c}={\begin{cases}0,&{\text{if }}c>r,\\{\dbinom {r-1}{c-1}}h^{r-c}d^{c-1}&{\text{if }}c\leq r.\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2748d6e4860b739b87faea4b7eb9b6b6a57c701d)
![{\displaystyle [{\vec {V}}(n)]_{r}={\begin{cases}1,&{\text{if }}r=1,\\n^{r-1}&{\text{if }}r>1.\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7e286bbc9cc8fe596565db7c1f3387ab7820d29)
![{\displaystyle [{\vec {S}}_{h,d}(n)]_{r}={\begin{cases}n,&{\text{if }}r=1,\\\sum _{k=0}^{n-1}(h+kd)^{r-1}&{\text{if }}r>1.\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef4348a57e68c42a32937fd62df040d05cd4c35b)
0 references
Polynomials calculating sums of powers of arithmetic progressions
0 references