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True or False Logarithm
#1
Hey,

the following function iapproaches - if the limit exists - the intuitive logarithm to base , i.e. the intuitive Abel function of developed at 1:



The question is whether this is indeed the logarithm, i.e. if for , provided that the limit exists at all.

It has a certain similarity to Euler's false logarithm series (pointed out by Gottfried here) as it can indeed be proven that for natural numbers (even for in difference to Euler's series):


if we now utilize that for then we get



Hence


But is this true also for non-integer ? Do we have some rules like , or even ?
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Messages In This Thread
True or False Logarithm - by bo198214 - 07/27/2010, 04:53 AM
RE: True or False Logarithm - by Gottfried - 07/27/2010, 01:12 PM
RE: True or False Logarithm - by Gottfried - 07/27/2010, 02:41 PM
RE: True or False Logarithm - by bo198214 - 08/11/2010, 02:37 AM
RE: True or False Logarithm - by andydude - 04/25/2012, 09:37 PM

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