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 changing terminology (was: overview paper co-author invitation) Base-Acid Tetration Fellow Posts: 94 Threads: 15 Joined: Apr 2009 08/22/2009, 05:50 PM (This post was last modified: 08/22/2009, 11:57 PM by Base-Acid Tetration.) Uh Oh I saw a problem with the f-logarithm terminology. What if it can mean a function/operator being plugged into the exp's Taylor series (powers meaning iteration)? Someone might call THAT a functional exponential, in analog to the matrix exponential... consider this example (just an example, don't say it's circular because i use exp's taylor series) this statement of analyticity of a function: Iff the following statement holds true for all $x, x_0 \in U:$ $f(x) = e^{(x-x_0)\frac{d}{dx}}[f](x_0),$ then the function is analytic in $U.$ Can you call such a usage an operator exponential? Annotation: if you're confused about my example: (x-x0) is scalar multiplication by x-x0, and d/dx is the differentiation operator ... so $e^{(x-x_0)\frac{d}{dx}} = \sum^\infty_{n=0}\frac{1}{n!} (x-x_0)^n \frac{d^n}{dx^n}$ Apply that to f, and you get: $e^{(x-x_0)\frac{d}{dx}}[f] = \sum^\infty_{n=0}\frac{(x-x_0)^n}{n!} \frac{d^n f}{dx^n}$ "Plug in" x_0 to this resulting function: $e^{(x-x_0)\frac{d}{dx}}[f](x_0) = \sum^\infty_{n=0}\frac{(x-x_0)^n}{n!} f^{(n)} (x_0)= \sum^\infty_{n=0} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n$. « Next Oldest | Next Newest »

 Messages In This Thread changing terminology (was: overview paper co-author invitation) - by andydude - 08/03/2009, 12:41 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/10/2009, 05:09 PM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/10/2009, 05:51 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/10/2009, 06:12 PM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/11/2009, 01:38 AM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/11/2009, 02:17 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/11/2009, 02:37 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/10/2009, 06:15 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/10/2009, 07:04 PM RE: changing terminology (was: overview paper co-author invitation) - by Gottfried - 08/10/2009, 10:03 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/11/2009, 12:06 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/11/2009, 02:14 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/11/2009, 01:45 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/11/2009, 01:56 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/13/2009, 09:51 AM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/13/2009, 10:55 AM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/13/2009, 11:20 AM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/13/2009, 07:53 PM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/13/2009, 09:21 PM RE: changing terminology (was: overview paper co-author invitation) - by bo198214 - 08/13/2009, 10:17 PM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/14/2009, 09:34 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/13/2009, 07:34 PM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/22/2009, 05:50 PM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 08/23/2009, 12:46 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 08/23/2009, 02:07 PM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 09/02/2009, 05:01 PM RE: changing terminology (was: overview paper co-author invitation) - by andydude - 11/04/2009, 03:24 AM RE: changing terminology (was: overview paper co-author invitation) - by Base-Acid Tetration - 11/05/2009, 02:06 AM RE: overview paper co-author invitation - by Base-Acid Tetration - 08/03/2009, 06:10 PM RE: overview paper co-author invitation - by bo198214 - 08/04/2009, 04:46 PM RE: overview paper co-author invitation - by Gottfried - 08/04/2009, 07:13 PM RE: overview paper co-author invitation - by sheldonison - 08/04/2009, 09:17 PM RE: overview paper co-author invitation - by Kouznetsov - 08/05/2009, 08:16 AM RE: overview paper co-author invitation - by andydude - 08/13/2009, 09:05 AM RE: overview paper co-author invitation - by bo198214 - 08/13/2009, 09:22 AM RE: overview paper co-author invitation - by jaydfox - 08/05/2009, 05:51 PM RE: overview paper co-author invitation - by bo198214 - 08/05/2009, 06:15 PM RE: overview paper co-author invitation - by jaydfox - 08/05/2009, 06:25 PM RE: overview paper co-author invitation - by bo198214 - 08/05/2009, 06:51 PM RE: overview paper co-author invitation - by Gottfried - 08/05/2009, 07:54 PM RE: overview paper co-author invitation - by Kouznetsov - 08/06/2009, 02:36 AM

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