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 Matrix Operator Method Gottfried Ultimate Fellow Posts: 757 Threads: 116 Joined: Aug 2007 04/18/2008, 01:55 PM (This post was last modified: 04/18/2008, 01:57 PM by Gottfried.) I've got some mail, where the author considered the case from the view of generation-functions, which may be interesting for a needed proof of the method. Here some exchange: Code:```It seems that e.g.f. of your triangle is: (exp(y*(exp(y*(exp(x)-1))-1))-1)/y^2 which gives 1, 1,1,1, 1,3,4,3,1, 1,7,13,19,13,6,1, ...```Next mail: Code:```And the e.g.f. connected to your coefficient a_3() is (exp(y*(exp(y*(exp(y*(exp(x)-1))-1))-1))-1)/y^3 which gives triangle 1, 1,1,1,1, 1,3,4,6,4,3,1, 1,7,13,26,31,31,25,13,6,1, ... And so on.```Then I did not understand, how the generation-function was related to the bivariate array: Code:```´ > However, I did not understand how you arrived > via the generation-function process at the > actual K-matrices. Would you mind to explain > this to me? > > Gottfried```Final mail: Code:```An example: Substituting t = exp(y)  in  your U_t(x,2) we get exp(y*(exp(y*(exp(x)-1))-1))-1 = y^2*x+(1/2*y^2+1/2*y^3+1/2*y^4)*x^2+(1/6*y^2+1/2*y^3+2/3*y^4+1/2*y^5+1/6*y^6)*x^3+(1/24*y^2+7/24*y^3+13/24*y^4+19/24*y^5+13/24*y^6+1/4*y^7+1/24*y^8)*x^4+... .``` Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Matrix Operator Method - by Gottfried - 08/12/2007, 08:08 PM RE: Matrix Operator Method - by bo198214 - 08/13/2007, 04:15 AM RE: Matrix Operator Method - by jaydfox - 08/13/2007, 05:40 AM RE: Matrix Operator Method - by Gottfried - 08/13/2007, 09:22 AM RE: Matrix Operator Method - by bo198214 - 08/14/2007, 03:43 PM RE: Matrix Operator Method - by Gottfried - 08/14/2007, 04:15 PM RE: Matrix Operator Method - by bo198214 - 08/26/2007, 12:18 AM RE: Matrix Operator Method - by Gottfried - 08/26/2007, 11:24 AM RE: Matrix Operator Method - by bo198214 - 08/26/2007, 11:39 AM RE: Matrix Operator Method - by Gottfried - 08/26/2007, 04:22 PM RE: Matrix Operator Method - by Gottfried - 08/26/2007, 10:54 PM RE: Matrix Operator Method - by bo198214 - 08/27/2007, 08:29 AM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 11:04 AM RE: Matrix Operator Method - by bo198214 - 08/27/2007, 11:35 AM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 11:58 AM RE: Matrix Operator Method - by bo198214 - 08/27/2007, 12:13 PM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 01:19 PM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 02:29 PM RE: Matrix Operator Method - by bo198214 - 08/27/2007, 02:36 PM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 03:09 PM RE: Matrix Operator Method - by bo198214 - 08/27/2007, 07:15 PM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 08:15 PM RE: Matrix Operator Method - by bo198214 - 08/29/2007, 05:28 PM RE: Matrix Operator Method - by Gottfried - 08/27/2007, 12:43 PM RE: Matrix Operator Method - by Gottfried - 10/08/2007, 12:11 PM RE: Matrix Operator Method - by Gottfried - 10/14/2007, 09:32 PM RE: Matrix Operator Method - by Gottfried - 04/04/2008, 09:41 AM RE: Matrix Operator Method - by Gottfried - 04/17/2008, 09:21 PM RE: Matrix Operator Method - by bo198214 - 04/25/2008, 03:39 PM RE: Matrix Operator Method - by Gottfried - 04/26/2008, 06:09 PM RE: Matrix Operator Method - by bo198214 - 04/26/2008, 06:47 PM RE: Matrix Operator Method - by Gottfried - 04/18/2008, 01:55 PM RE: Matrix Operator Method - by Gottfried - 07/08/2008, 06:46 AM Diagonalization for dxp/basic facts/Pari-routine - by Gottfried - 08/08/2008, 01:12 PM Exact entries for T-tetration Bell-matrix - by Gottfried - 09/24/2008, 08:22 PM RE: Exact entries for T-tetration Bell-matrix - by bo198214 - 09/26/2008, 07:30 AM RE: Exact entries for T-tetration Bell-matrix - by Gottfried - 09/26/2008, 09:56 AM

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