Confluent hypergeometric function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Confluent hypergeometric function" in English language version.

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ams.org

Campos, L.M.B.C. (2001). "On Some Solutions of the Extended Confluent Hypergeometric Differential Equation". Journal of Computational and Applied Mathematics. 137 (1): 177–200. Bibcode:2001JCoAM.137..177C. doi:10.1016/s0377-0427(00)00706-8. MR 1865885.
Frank, Evelyn (1956). "A new class of continued fraction expansions for the ratios of hypergeometric functions". Trans. Am. Math. Soc. 81 (2): 453–476. doi:10.1090/S0002-9947-1956-0076937-0. JSTOR 1992927. MR 0076937.

Campos, L.M.B.C. (2001). "On Some Solutions of the Extended Confluent Hypergeometric Differential Equation". Journal of Computational and Applied Mathematics. 137 (1): 177–200. Bibcode:2001JCoAM.137..177C. doi:10.1016/s0377-0427(00)00706-8. MR 1865885.
Frank, Evelyn (1956). "A new class of continued fraction expansions for the ratios of hypergeometric functions". Trans. Am. Math. Soc. 81 (2): 453–476. doi:10.1090/S0002-9947-1956-0076937-0. JSTOR 1992927. MR 0076937.

Campos, L.M.B.C. (2001). "On Some Solutions of the Extended Confluent Hypergeometric Differential Equation". Journal of Computational and Applied Mathematics. 137 (1): 177–200. Bibcode:2001JCoAM.137..177C. doi:10.1016/s0377-0427(00)00706-8. MR 1865885.

Frank, Evelyn (1956). "A new class of continued fraction expansions for the ratios of hypergeometric functions". Trans. Am. Math. Soc. 81 (2): 453–476. doi:10.1090/S0002-9947-1956-0076937-0. JSTOR 1992927. MR 0076937.

This is derived from Abramowitz and Stegun (see reference below), page 508, where a full asymptotic series is given. They switch the sign of the exponent in $exp(iπa)$ in the right half-plane but this is immaterial, as the term is negligible there or else $a$ is an integer and the sign doesn't matter.