0,2

This is based on the derivatives of the real function g(x) := -1/f(x)^2. They have been generated using the software Mathematica. I'm trying to find a closed form.

I have the complete program code and can send it to anyone interested.

H. Sussmann, Resultats recents sur les courbes optimales, Soc. Math. de France du 17 juin 2000

H. Sussmann and J. C. Willems, 300 Years of Optimal Control - IEEE Control Systems 1997 0272-1708l97l$10.0001997IEEE

H. Sussmann and J. C. Willems, The Brachistochrone Problem and Modern Control Theory - University of Groningen, May 1999

Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/UmbralCalculus.html

Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/GeneratingFunction.html

Eric Weisstein's World of Mathematics, http://mathworld.wolfram.com/CauchyProduct.html

The algorithm for the sequence is as follows: (step#) What to do (1) Dj = 0, for each j, when j is odd (j=2k+1); (odd derivatives are null) (3) D2 = -1*f(a)^-2; then b1 = 1; (the 2nd derivative) (4) D4 = -2*f(a)^-5; (the 4th derivative) So b2 = 2; (5) D6 = -22*f(a)^-8; (the 6th derivative) So b3 = 22; (6) D8 = -584*f(a)^-11 (the 8th derivative) So b4 = 584; (8) D10= -28384*f(a)^-14 (the 10th derivative) So b5 = 28384; and so on... (n) D2n= -bn*f(a)^-(3n-1) (the 2n-th derivative) on general bn is unknown.

Sequence in context: A090730 A090313 A110129 this_sequence A132568 A015210 A152558

Adjacent sequences: A120416 A120417 A120418 this_sequence A120420 A120421 A120422

uned,nonn,obsc,more

Robert Wackensack (wackensack(AT)hotmail.com), Jul 09 2006