Tag Archives: reciprocal sums and series

Catalanization


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Filed under Catalan numbers, differential equations, math analysis, sum of reciprocals

another reciprocal sum problem


ok we already know how to calculate how many rationals, \mathbb{Q}, exists in terms of the height function

h(a/b)=\max (|a|,|b|)

gcd(a,b)=1

It turns out that the A171503  entry of the OEIS tells more…

http://192.20.225.10/~njas/sequences/A171503

meanwhile it is natural to ask for convergence of

1/3 + 1/7 + 1/15 + 1/23 + 1/31 + 1/47 + 1/71 + 1/87 + 1/111 + 1/127+...

and for (non-) existence of a generating function…

The crescent sequence could be called Siehler’s numbers

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reciprocal Catalan numbers


the subject that gives the grade of B.Sc. to my ex-pupil and friend, was originated making a conjecture that in less than of a month we will know how to demonstrate the formula in

http://www.research.att.com/~njas/sequences/A121839

but we were even able of finding a generating function for them

Congratulations David!

… this function is:

or \frac{2\sqrt{4-x}(8+x)+12\sqrt{x}\arctan{\frac{\sqrt{x}}{\sqrt{4-x}}}}{\sqrt{(4-x)^5}}

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