laguerre_polynomials.sf 490 B

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  1. #!/usr/bin/ruby
  2. # Closed-form for Laguerre polynomials.
  3. # See also:
  4. # https://en.wikipedia.org/wiki/Laguerre_polynomials
  5. # https://mathworld.wolfram.com/LaguerrePolynomial.html
  6. func laguerre_polynomial(n, x) {
  7. sum(0..n, {|k|
  8. (-1)**k * binomial(n, k) * x**k / k!
  9. })
  10. }
  11. for n in (1..20) {
  12. say laguerre_polynomial(4, 6*n)
  13. }
  14. __END__
  15. -5
  16. 97
  17. 1387
  18. 6241
  19. 18331
  20. 42625
  21. 85387
  22. 154177
  23. 257851
  24. 406561
  25. 611755
  26. 886177
  27. 1243867
  28. 1700161
  29. 2271691
  30. 2976385
  31. 3833467
  32. 4863457
  33. 6088171
  34. 7530721