Dear Wolfram Community!

I typed the following into Wolfram Mathematica: FullSimplify[ 1/(Gamma[a]^2Gamma[1 - a]) * Integrate[ HypergeometricU[1, 1, zk]k^(a - 1)(1 - k)^(-a), {k, 0, 1}]] and I get this answer: ConditionalExpression[HypergeometricU[a, 1, z], 0 < Re[a] < 1].

I would like to used this identity in my article, but I cannot find such relation in the literature: Slater, L.J. (1960). Confluent hypergeometric functions. Cambridge University Press. Bateman, H. Erdelyi, A. (1953). Higher Transcendental Functions. Vol 1. McGraw-Hill. Abramowitz, M., Stegun, I. (1970). Handbook of Mathematical Functions. Dover.

Could I look somehow how the Wolfram Mathematica calculate this identity, and how can I refer such a calculation in my article?

I would appreciate any ideas or hint.