Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
binomial_coefficient_over_the_complex_numbers [2016/05/12 19:21] nikolaj |
binomial_coefficient_over_the_complex_numbers [2016/08/21 11:33] nikolaj |
||
|---|---|---|---|
| Line 5: | Line 5: | ||
| ----- | ----- | ||
| + | $(1+z)^s$ | ||
| + | |||
| + | Sum[Gamma[1 + x]/(Gamma[1 + x - y] Gamma[1 + y])z^y, {y, 0, \[Infinity]}] | ||
| + | |||
| === Discussion === | === Discussion === | ||
| For natural numbers $n\ge{k}$ we get | For natural numbers $n\ge{k}$ we get | ||
| Line 21: | Line 25: | ||
| <code> | <code> | ||
| - | (* Random generalization of linear such recursive schemes *) | + | (*Random generalization of linear such recursive schemes*) |
| - | F[m_, 0] = a; | + | f[m_, 0] = a[m]; |
| - | F[0, m_] = b; | + | f[0, m_] = b[m]; |
| - | F[m_, m_] = c; | + | f[m_, m_] = c[m]; |
| - | F[n_, k_] := A*F[n, k - 1] + B*F[n - 1, k] + C*F[n - 1, k - 1] | + | f[n_, k_] := A*f[n, k - 1] + B*f[n - 1, k] + C*f[n - 1, k - 1] |
| - | Table[{n, k, F[n, k]}, {n, 0, 4}, {k, 0, 4}] // TableForm | + | Table[{n, k, f[n, k] // sexy}, {n, 1, 4}, {k, 1, 4}] // TableForm |
| </code> | </code> | ||
