Gamma Derivative Twice!

Using the digamma function's definition, $\psi \left( x \right) =\frac { \Gamma ^{ \prime }\left( x \right) }{ \Gamma \left( x \right) } \\ \Gamma ^{ \prime }\left( x \right) =\psi \left( x \right) \Gamma \left( x \right) \\ \frac { d }{ dx } \left( \Gamma ^{ \prime }\left( x \right) \right) =\frac { d }{ dx } \left( \psi \left( x \right) \Gamma \left( x \right) \right) \\ \Gamma ^{ \prime \prime }\left( x \right) ={ \psi }_{ 1 }\left( x \right) \Gamma \left( x \right) +\psi \left( x \right) \Gamma ^{ \prime }\left( x \right) \quad using\quad product\quad rule\\ ={ \psi }_{ 1 }\left( x \right) \Gamma \left( x \right) +{ \psi \left( x \right) }^{ 2 }\Gamma \left( x \right)$

if $x=3$

$\\ { \psi }_{ 1 }\left( 3 \right) \Gamma \left( 3 \right) +{ \psi \left( 3 \right) }^{ 2 }\Gamma \left( 3 \right) =\left( \frac { { \pi }^{ 2 } }{ 6 } -\frac { 5 }{ 4 } \right) \times 2+{ \left( \frac { 3 }{ 2 } -\gamma \right) }^{ 2 }\times 2\\ =\frac { { \pi }^{ 2 } }{ 3 } -\frac { 5 }{ 2 } +\frac { 9 }{ 2 } -6\gamma +2{ \gamma }^{ 2 }\\ =2+2{ \gamma }^{ 2 }+\frac { { \pi }^{ 2 } }{ 3 } -6\gamma$

so $2+2+3+2+6+2=17$