<fart>
Does your ass booty-juice?
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"galathaea" <galathaea@[EMAIL PROTECTED]
> wrote in message
news:1167539453.289817.272460@[EMAIL PROTECTED]
>
> galathaea wrote:
>> i have always been suspicious of the hidden 1
>>
>> or rather
>> the hidden (1)_i
>> in hypergeometric F notation
>>
>> it seemed
>> not well hidden
>>
>> and not very useful
>>
>> if i want to represent
>>
>> oo
>> --- i
>> \ x
>> / -----
>> --- ( a )
>> i = 0 i
>>
>> i must insert the numerator (1)_i
>> and the denominator (1)_i
>>
>> to get
>>
>> / 1 \
>> F | ; x |
>> 1 2 \ a, 1 /
>
> actually
> her illusions had confused me
>
> and i meant to hide her in the bottom
>
>> / 1 \
>> F | ; x |
>> 1 1 \ a /
>
> but was enraged until i had to reveal her form
>
> but she mocks from above anyhow
>
>>
>> and that disturbs me
>>
>
>> -+-
>>
>> i have recently been able to prove
>> to my satisfaction
>> that the (1)_i
>>
>> is actually a goddess placed in the notation by gauss
>> to deceive and beguile the initiates
>>
>> -Z-Z-Z-Z-z-z-z-
>>
>> the differential equation form
>> revealed her for the obvious imposter
>>
>> defining the point transformation operator
>>
>> d
>> D = x --
>> dx
>>
>> the product formula
>>
>> D ( D + b0 - 1 ) ( D + b1 - 1 ) ... ( D + b(q-1) - 1 ) F
>>
>> = x ( D + a0 ) ( D + a1 ) ... ( D + a(p-1) ) F
>>
>> is satisfied by
>>
>> _\
>> / a \
>> F | _\ ; x |
>> p q \ b /
>>
>> where now a and b are vectors
>>
>> _\
>> a = ( a0, a1, ..., a(p-1) )
>>
>> _\
>> b = ( b0, b1, ..., b(q-1) )
>>
>>
>>
>> $^$*#$*^#(#()%)^(%^$*@[EMAIL PROTECTED]
>>
>>
>> not only does she stand there in the product formula
>> for all eyes to see
>> but one discovers her name as well
>>
>> D
>>
>> the one on the leftend in the first line of the formula
>>
>> D is (1)_i
>>
>> so like parvati is kali
>> we have her pinned
>>
>>
>> ~~~~~~~~~~~~~~~~~o
>>
>> but i only truly understood
>> the nature of her beguiling
>> after i decided to transform my multisection results
>> to goddess-free notation
>> because i suspected her influence
>>
>> in the beguiled notation
>> my multisection theorems relate
>> the (m, n)-multisection of a (p, q)-hypergeometric
>> to a ( p n + 1, q ( n + 1 ) )-hypergeometric
>> which can be reduced to ( p n, q ( n + 1 ) - 1 )
>>
>> but the (p, q)-atheistic hypergeometric is defined as
>>
>> _\
>> / a \
>> H | _\ ; x | =
>> p q \ b /
>>
>> p-1
>> oo --- oo
>> --- | | ( aj ) --- _\
>> \ j=0 i i \ / a \
>> / ------------- x = / h | _\ ; x |
>> --- q-1 --- i \ b /
>> i = 0 --- i = 0
>> | | ( bk )
>> k=0 i
>>
>> in this goddess-free formulation
>> the multisection is simply
>>
>> _\
>> |m / a \
>> | H | _\ ; x | =
>> |n p q \ b /
>>
>>
>> _\ |m _\
>> / a \ / |n a / x \ n \
>> h | _\ ; x | H | |m _\ ; | --- | |
>> m \ b / pn qn \ |n b \ q-p / /
>> n
>>
>> where
>>
>> p-1 n-1
>> |m _\ _ _ / ai + m + j \
>> |n a = (x) (x) | ---------- |
>> - - \ n /
>> i=0 j=0
>>
>> and
>> q-1 n-1
>> |m _\ _ _ / bi + m + j \
>> |n b = (x) (x) | ---------- |
>> - - \ n /
>> i=0 j=0
>>
>> this is radiantly clear
>>
>> -+-+-+-+-
>>
>> the key to the goddess' spell
>> is her obfuscation of the vector spaces involved
>>
>>
>> +X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+
>>
>> to demonstrate this atheistic notation
>> in the formulagenic uses of the multisection theorem
>>
>> the fundament of circularre geometrie
>>
>> x
>> y = e
>>
>> manifests the goddess explicitly as
>>
>> / - \
>> H | ; x |
>> 0 1 \ 1 /
>>
>>
>> the fundamental level-2 multisection theory
>> gives us the 3 relations
>>
>> x |0 x |1 x
>> e = | e + | e
>> |2 |2
>>
>> |0 x 1 x -x
>> | e = - ( e + e )
>> |2 2
>>
>> |1 x 1 x -x
>> | e = - ( e - e )
>> |2 2
>>
>> which hypergeometric multisection represents as
>>
>> |0 / - \ / - / x \2 \
>> | H | ; x | = H | ; | - | |
>> |2 0 1 \ 1 / 0 2 \ 1/2, 1 \ 2 / /
>>
>>
>> |1 / - \ / - / x \2 \
>> | H | ; x | = x H | ; | - | |
>> |2 0 1 \ 1 / 0 2 \ 1, 3/2 \ 2 / /
>>
>> and substituting into the above
>> provides the 3 projection relations of level 2
>>
>> now using these in conjunction with
>> contiguous relations
>> allows us to derive a number
>> of famous hypergeometric relation****ps
>> involving the rational subspaces of the coefficient space
>>
>> taking x at known values
>> provides a foundation for calculating
>> relation****ps for all unit-related values
>> scaled by the power term
>>
>> we can apply the above to the classic gaussian
>> for instance
>> which atheistically is expressed as
>>
>> / a, b \
>> H | ; x |
>> 2 2 \ c, 1 /
>>
>> the level-2 multisection projections are
>>
>> |0 / a, b \
>> | H | ; x | =
>> |2 2 2 \ c, 1 /
>>
>> / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> H | ; x |
>> 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> and
>>
>> |1 / a, b \
>> | H | ; x | =
>> |2 2 2 \ c, 1 /
>>
>> ab / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> -- x H | ; x |
>> c 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> plugging into the basic level 2 forms gives
>>
>>
>> (*)
>> / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> H | ; x | +
>> 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> ab / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> -- x H | ; x | =
>> c 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> / a, b \
>> H | ; x |
>> 2 2 \ c, 1 /
>>
>> (a)
>> / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> H | ; x | =
>> 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> 1 / / a, b \ / a, b \ \
>> - | H | ; x | + H | ; -x | |
>> 2 \ 2 2 \ c, 1 / 2 2 \ c, 1 / /
>>
>> (b)
>>
>> ab / a/2, (a+1)/2, b/2, (b+1)/2 2 \
>> -- x H | ; x | =
>> c 4 4 \ c/2, (c+1)/2, 1/2, 1 /
>>
>> 1 / / a, b \ / a, b \ \
>> - | H | ; x | - H | ; -x | |
>> 2 \ 2 2 \ c, 1 / 2 2 \ c, 1 / /
>>
>> and there are places gauss' form can be evaluated
>> such as at 1
>> providing explicit reflection formuli
>>
>> ^**^ ^**^ ^**^ ^**^ ^**^
>>
>> by defeating the goddess
>> i had revealed the valuable secret
>> of clarity in form
>>
>> and could safely banish it from the empire
>>
>> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>> galathaea: prankster, fablist, magician, liar
>
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