# an integral involves mutiply of two Kummer Confluent Hypergeometric function

i met an integral involving the mutiply of two Kummer Confluent Hypergeometric functions as follows: $$\int_{ - \infty }^\infty {\frac{1}{{{x^\alpha }{{\left( {x + k} \right)}^\beta }}}{}_1{F_1}\left( {{a_1};{b_1};\frac{{{c_1}}}{x}} \right){}_1{F_1}\left( {{a_2};{b_2};\frac{{{c_2}}}{{x + k}}} \right)} dx$$ where ${}_1{F_1}$ is the Kummer Confluent Hypergeometric function, and $\alpha ,\beta ,{a_1},{a_2},{c_1},{c_2} > 0$. Thanks for your help in advance.

• Are you expecting a general closed form? Or asymptotics/numerics? – user111187 Dec 8 '14 at 9:54
• Thanks for your attention, i need a closed-form expression. – Chaoqing Tang Dec 8 '14 at 11:32
• @ChaoqingTang Are any of the constants integer? – rrogers Oct 7 '15 at 13:54