Lacunary ogf of Laguerre's

[Karol PENSON]

      Dear Max thank a lot, it works !!!!, I have checked with Maple  . 
Karol

Max Alekseyev wrote:

> Karol,
>
> Look at formula (7) at 
> http://mathworld.wolfram.com/LaguerrePolynomial.html
> It implies that
> sum(z^(2*n)*LaguerreL(2*n,x),n=0..infinity) = (g(x,z) + g(x,-z)) / 2 =
> (exp(-xz/(1-z))/(1-z) + exp(xz/(1+z))/(1+z)) / 2
> Now to get sum(t^n*LaguerreL(2*n,x),n=0..infinity) make a substitution 
> z^2 = t.
>
> Max
>
> On 6/27/06, Karol PENSON <penson at lptl.jussieu.fr> wrote:
>
>>
>>
>>
>>    Dear Seqfans,
>>  Does anyone know a closed form expression for the double-lacunary, 
>> ordinary
>> generating function
>>  of Laguerre polynomials, i.e. , in Maple notation, for
>>
>>                                   sum(t^n*LaguerreL(2*n,x),
>> n=0..infinity) ?
>>
>>
>>  Thanks ,      Karol A. Penson --
>> _________________________________________________________________________ 
>>
>> Karol A. PENSON
>> Universite Paris 6 | Internet : penson at lptl.jussieu.fr.
>> Lab. Physique Theorique des |
>> Liquides | http://www.lptl.jussieu.fr/users/penson
>> Boite courrier 121 |
>> 4, place Jussieu, Tour 24, Et.4 | Tel : (33 1) 44 27 72 33
>> 75252 Paris Cedex 05, France | Fax : (33 1) 44 27 51 00
>>
>>


-- 
_________________________________________________________________________
Karol A. PENSON
Universite Paris 6              |  Internet : penson at lptl.jussieu.fr.
Lab. Physique Theorique des     |
Liquides                        | http://www.lptl.jussieu.fr/users/penson
Boite courrier 121              |
4, place Jussieu, Tour 24, Et.4 |      Tel : (33 1) 44 27 72 33
75252 Paris Cedex 05, France    |      Fax : (33 1) 44 27 51 00