Multiply a Laguerre series by x. Multiply the Laguerre series `c` by x, where x is the independent variable. Parameters ---------- c : array_like 1-D array of Laguerre series coefficients ordered from low to high. Returns ------- out : ndarray
(c)
| 386 | |
| 387 | |
| 388 | def lagmulx(c): |
| 389 | """Multiply a Laguerre series by x. |
| 390 | |
| 391 | Multiply the Laguerre series `c` by x, where x is the independent |
| 392 | variable. |
| 393 | |
| 394 | |
| 395 | Parameters |
| 396 | ---------- |
| 397 | c : array_like |
| 398 | 1-D array of Laguerre series coefficients ordered from low to |
| 399 | high. |
| 400 | |
| 401 | Returns |
| 402 | ------- |
| 403 | out : ndarray |
| 404 | Array representing the result of the multiplication. |
| 405 | |
| 406 | See Also |
| 407 | -------- |
| 408 | lagadd, lagsub, lagmul, lagdiv, lagpow |
| 409 | |
| 410 | Notes |
| 411 | ----- |
| 412 | The multiplication uses the recursion relationship for Laguerre |
| 413 | polynomials in the form |
| 414 | |
| 415 | .. math:: |
| 416 | |
| 417 | xP_i(x) = (-(i + 1)*P_{i + 1}(x) + (2i + 1)P_{i}(x) - iP_{i - 1}(x)) |
| 418 | |
| 419 | Examples |
| 420 | -------- |
| 421 | >>> from numpy.polynomial.laguerre import lagmulx |
| 422 | >>> lagmulx([1, 2, 3]) |
| 423 | array([-1., -1., 11., -9.]) |
| 424 | |
| 425 | """ |
| 426 | # c is a trimmed copy |
| 427 | [c] = pu.as_series([c]) |
| 428 | # The zero series needs special treatment |
| 429 | if len(c) == 1 and c[0] == 0: |
| 430 | return c |
| 431 | |
| 432 | prd = np.empty(len(c) + 1, dtype=c.dtype) |
| 433 | prd[0] = c[0] |
| 434 | prd[1] = -c[0] |
| 435 | for i in range(1, len(c)): |
| 436 | prd[i + 1] = -c[i]*(i + 1) |
| 437 | prd[i] += c[i]*(2*i + 1) |
| 438 | prd[i - 1] -= c[i]*i |
| 439 | return prd |
| 440 | |
| 441 | |
| 442 | def lagmul(c1, c2): |