I would like to relate the following hypergeometric 2F2 function:

$\,_2F_2 \left(1, n+1-\alpha;n+2,n+2-\alpha-\beta;-x\right)$,

where $\alpha,\beta>0$ to another 2F2 function:

$\,_2F_2 \left(n+1,\alpha;n+2,1+\alpha+\beta;x\right)$.

I would be very grateful if someone could help out.


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