Re: inversehypergeometric !

On Jun 6, 4:09 pm, tommy1729 <tommy1...@xxxxxxxxx>
wrote:
While "studying" hypergeometric functions, I've
noticed
them having an inverse witch is also
hypergeometric.

usually easy to find.

but is this always so ?

which algoritm can be used to do the inverse ??

forgive my low level of knowledge of these
important functions.

this really depends upon what you consider
hypergeometric form

take the hypergeometric goddess in here bare form

x / \
e = F | - ; x |
0 0 \ /

this is prototypical in many ways

now the inverse
the logarithm
cannot be expanded around zero

so in that sense it cannot be hypergeometric
in that it cannot be put in the form

--- ---
\ | | (a_j)_i i
/ ------------ x
--- ---
i | | (b_k)_i

however
if you allow the variable term to be more
re expressive

/ 1, 1 \
ln x = F | ; 1-x |
\ 2 /

but notice that this is a loose interpretation
because 1 + x is hypergeometric
and if we allow x to be substituted with anything
we can make anything
and the statement that inverses can be expressed
becomes meaningless

so you have to choose a standard form
before such a statement can make sense

now it is possible to make a stronger statement on
the forms
and i have in previous posts shown one proof
but the exposition is pretty long
and relies on some projection theorems

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar


i understand that series cant always be expanded everywhere.
and i accept any form of hypergeo.

plz tell me more

tommy1729

ps your notation is confusing :s
but thanks for trying.
.