Re: B(x) = 2^-x + B(4x/3) + B((2x-1)/3) + B(4x+2)
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Re: B(x) = 2^-x + B(4x/3) + B((2x-1)/3) + B(4x+2)         


Author: Frederick Umminger
Date: Jul 18, 2006 11:45

"Eighty" gmail.com> wrote in message
news:1153145547.399026.164570@s13g2000cwa.googlegroups.com...
>
> James Dow Allen wrote:
>> This may be an old problem.
>>
>> Let B(x) be a function such that
>> If x is not an integer
>> B(x) = 0
>> If x is an integer
>> B(x) = 2^-x + B(4x/3) + B((2x-1)/3) + B(4x+2)
>> Prove (or disprove) that
>> B(2) = 1
>>
>>
>> James Dow Allen
>
> No one has said anything in this thread for a while; could you give us
> the answer?
> ...
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Re: B(x) = 2^-x + B(4x/3) + B((2x-1)/3) + B(4x+2)         


Author: Patrick Coilland
Date: Jul 18, 2006 11:54

Frederick Umminger nous a récemment amicalement signifié :
>
> Let x = 0
>
> B(2) = B(0) - 2^-0 - B(0) - B(-1/3)
> B(2) = -1 - B(-1/3)
> B(2) = -1
>
> since B(y) = 0 if y is not an integer
>

Unfortunatly, OP did not accept this solution (first given by william
Elliot) :

This assumes that B(0) is defined, and that the definition is
consistent. This is a claim I did not intend to make


So, OP wants us to demonstrate that his definition is consistent (or
not).

This is the reason for which we all are interested in his demonstration
of (in)consistancy.
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