Question: hypergeometric functions

in reference to the definition prescribed in the maple help interface and the attached worksheet, i cant understand how hypergeom(n,d,z) handles empty values of the lists n,d eg hypergeom([],[],pi)  
 

hypergeom([n[1], n[2], n[3], () .. (), n[p]], [d[1], d[2], d[3], () .. (), d[q]], z) = sum(z^k*(product(GAMMA(k+n[i])/GAMMA(n[i]), i = 1 .. p))/(factorial(k)*(product(GAMMA(k+d[j])/GAMMA(d[j]), j = 1 .. q))), k = 0 .. infinity)


 

Download maplePRIMEShypergeomQ.mw

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