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Type II Confluent Hypergeometric Function

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Calculate the second-kind confluent hypergeometric function U(a,b,z).
\(\normalsize Confluent\ Hypergeometric\ function\ of\ the\ 2nd\ kind\\ \hspace{30px} U(a,b,z)=\frac{\Gamma(1-b)}{\Gamma(a-b+1)}M(a,b,z)+\frac{\Gamma(b-1)}{\Gamma(a)}z^{1-b}M(a-b+1,2-b,z)\\ \)
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U(a,b,z) 
\(\normalsize Confluent\ hypergeometric\ differential\ equation\\ (1)\ zy''+(b-z)y'-ay=0\\ \hspace{25px} y=c_1M(a,b,z)+c_2U(a,b,z)\\ \)

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