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 using cosh(x) ? tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 11/19/2011, 11:56 PM no , im not kidding , apart from my sinh method im considering a cosh method. although it might be more complicated or speculative. it might be insightfull to plot things. consider exp(1/e) R. replace x by f(x) and let g(x) be the super of f(x). then we get a difference equation for g(x). we solve that difference equation , now we go from g(x) to f(x) or we find the taylor for f(x) from the equation ( or both , in programming ). similar to the sinh method : since f is close to 2*cosh(ln(b)*x)) and 2*cosh(ln(b)*x) is close to b^x , we have a new method. tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 11/20/2011, 12:01 AM also , we finally have boundaries. for large x , f^[1/2](x) + f^[1/2](ln_b(x)) is a good bound for tet(b,1/2,x). tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 11/20/2011, 10:57 AM (This post was last modified: 11/20/2011, 11:01 AM by tommy1729.) hmm i was thinking about f(x) - f[-1](x) = 2*sinh(ln(b)*x). for approximating (b^x)^[theta] for bases b with eta < b < sqrt(e) and x > e^e. tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 11/20/2011, 11:23 AM (This post was last modified: 11/20/2011, 11:36 AM by tommy1729.) a possible improvement would be f(x) - f^[-1](x) = 2*sinh(ln(b)*x) + (e-2)*x/e. f(0) = 0 tommy1729 sheldonison Long Time Fellow Posts: 683 Threads: 24 Joined: Oct 2008 11/20/2011, 03:18 PM (11/19/2011, 11:56 PM)tommy1729 Wrote: no , im not kidding , apart from my sinh method im considering a cosh method.What is the fixed point for this method? The fixed point for 2sinh was zero. tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 11/20/2011, 06:29 PM (11/20/2011, 03:18 PM)sheldonison Wrote: (11/19/2011, 11:56 PM)tommy1729 Wrote: no , im not kidding , apart from my sinh method im considering a cosh method.What is the fixed point for this method? The fixed point for 2sinh was zero. the fixed point is pi/2 i for the cosh method. for the ' new ' sinh method it is also 0. « Next Oldest | Next Newest »

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