 My Math Forum Function between constant functions and iterated logarithms

 Number Theory Number Theory Math Forum

 March 13th, 2011, 06:37 PM #1 Newbie   Joined: Mar 2011 Posts: 10 Thanks: 0 Function between constant functions and iterated logarithms I am looking for a continuous and increasing function f(x) which tends to infinity as x tends to infinity. This function must have the property that it is eventually smaller than log_k(x) (the k-th iterated logarithm) for all k>=1 I have no hint how to find such a function! One of my problems is that log_k(x) tends to 0 when k tends to infinity... then how is it possible to find f(x) increasing?! March 13th, 2011, 07:52 PM #2 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Function between constant functions and iterated logarit There's a function called log* that counts the number of times the logarithm must be taken to make the argument <= 1. This grows more slowly than any fixed number of logarithms, e.g. slower than log(log(log x)). Edit: You can make this continuous by adding the result after the logs. So the function would be x for x <= 1, 1 + log x for 1 < x <= e, 2 + log log x for e < x <= e^e, etc. Lots of other possibilities exist, of course. March 14th, 2011, 06:16 PM #3 Newbie   Joined: Mar 2011 Posts: 10 Thanks: 0 Re: Function between constant functions and iterated logarit Thanks a lot!!! It's really a nice function which possesses the properties I need! March 14th, 2011, 06:31 PM #4 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Function between constant functions and iterated logarit Glad to help! Out of curiosity, what is this for? March 16th, 2011, 07:05 PM #5 Newbie   Joined: Mar 2011 Posts: 10 Thanks: 0 Re: Function between constant functions and iterated logarit I used this in some work about the riemann zeta function Tags constant, function, functions, iterated, logarithms ### logs to find constant and function

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post FreaKariDunk Real Analysis 5 November 20th, 2012 02:00 PM RoyGBiv Complex Analysis 4 November 10th, 2011 04:01 PM baskabosyok Complex Analysis 3 August 23rd, 2011 07:08 AM snjvsingh Complex Analysis 1 April 20th, 2011 10:33 AM Simke Calculus 4 April 6th, 2011 01:06 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      