I have these three expressions
Gamma[1/2 + k]*Gamma[7/10 + k]*Gamma[9/10 + k]*Gamma[1 + k]^6*Gamma[11/10 + k]*
Gamma[13/10 + k]*Gamma[3/2 + k]*Gamma[17/10 + k]*Gamma[19/10 + k]*Gamma[21/10 + k]*
Gamma[23/10 + k]*Gamma[5/2 + k]*Gamma[13/5 + k]*Gamma[27/10 + k]*Gamma[29/10 + k]*
Gamma[3 + k]*Gamma[31/10 + k]*Gamma[33/10 + k]*Gamma[7/2 + k]*Gamma[18/5 + k]*
Gamma[37/10 + k]*Gamma[39/10 + k]*Gamma[41/10 + k]*Gamma[43/10 + k]*Gamma[9/2 + k]*
Gamma[23/5 + k]*Gamma[47/10 + k]*Gamma[49/10 + k]*Gamma[51/10 + k]*Gamma[53/10 + k]*
Gamma[28/5 + k]
and
Gamma[n]*Gamma[2/5 + n]^2*Gamma[3/5 + n]^3*Gamma[4/5 + n]^2*Gamma[5/6 + n]*
Gamma[7/6 + n]*Gamma[6/5 + n]^2*Gamma[7/5 + n]*Gamma[8/5 + n]^2*Gamma[9/5 + n]*
Gamma[11/6 + n]*Gamma[13/6 + n]*Gamma[11/5 + n]*Gamma[3 + 2*n]
and
Gamma[3/2 + k + n]*Gamma[17/10 + k + n]*Gamma[19/10 + k + n]*Gamma[2 + k + n]*
Gamma[21/10 + k + n]*Gamma[23/10 + k + n]*Gamma[5/2 + k + n]*Gamma[13/5 + k + n]*
Gamma[27/10 + k + n]*Gamma[29/10 + k + n]*Gamma[3 + k + n]*Gamma[31/10 + k + n]*
Gamma[33/10 + k + n]*Gamma[18/5 + k + n]
Also, relatedly
(1/10)*(23 + 10*n)*(1 + n)!*(2 + n)!*(1 + 2*n)!*(3 + 2*n)!*((1/10)*(7 + 10*n))!*
((1/10)*(9 + 10*n))!*((1/10)*(11 + 10*n))!*((1/10)*(13 + 10*n))!*((1/10)*(17 + 10*n))!*
((1/10)*(19 + 10*n))!*((1/10)*(21 + 10*n))!
To what extent can these be simplified?
n
andk
are integers),Gamma[2/5+n]^2 Gamma[7/5+n]
will simplify to(2/5+n) Gamma[2/5+n]^3
. $\endgroup$ – JimB Aug 22 '16 at 19:35