Timeline for Recurrent sequences and Bernoulli-like numbers
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2010 at 13:03 | history | edited | Johann Cigler | CC BY-SA 2.5 |
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| Dec 9, 2010 at 5:43 | history | edited | Johann Cigler | CC BY-SA 2.5 |
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| Dec 9, 2010 at 5:39 | comment | added | Johann Cigler | Yes of course. This is a typo. | |
| Dec 8, 2010 at 21:12 | comment | added | Aaron Meyerowitz | Well then did you mean $H_n(x,s)=xH_{n-1}(x,s)-(n-1)s H_{n-2}(x,s)?$ Otherwise I am not sure how the $x$ comes in. With that interpretation, More generally, given functions $u(n)$ and $v(n)$ (and initial conditions) let $A_n=A_n(u,v,s)$ be $$A_n=u(n)A_{n-1}+sv(n)A_{n-2}$$ In your two examples $(u,v)=(x,1)$ and $(u,v)=(x,n-1)$. | |
| Dec 8, 2010 at 20:15 | comment | added | Johann Cigler | Yes, $x$ should be a fixed number and $s$ the variable in order that the polynomials with even resp. odd indices form a basis of the vector space. | |
| Dec 8, 2010 at 20:14 | comment | added | Aaron Meyerowitz | Are you still thinking of $s$ as a formal variable for polynomials with $x$ as a parameter? That could make sense for $F_n$ but I don't see that $x$ does much of anything for $H_n$ | |
| Dec 8, 2010 at 16:42 | comment | added | j.c. | Is there a nice continued fraction interpretation of these identities? | |
| Dec 8, 2010 at 16:38 | history | edited | Johann Cigler | CC BY-SA 2.5 |
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| Dec 8, 2010 at 16:20 | history | edited | Johann Cigler | CC BY-SA 2.5 |
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| Dec 8, 2010 at 7:46 | answer | added | Aaron Meyerowitz | timeline score: 4 | |
| Dec 6, 2010 at 14:19 | history | asked | Johann Cigler | CC BY-SA 2.5 |