Horn function

In the theory of special functions in mathematics, the Horn functions are the 34 distinct convergent hypergeometric series of order two enumerated by J. Horn (1931) (as corrected by Borngässer in 1933). They are listed in (Erdélyi 1953, section 5.7.1).

References

• Borngässer, Ludwig (1933), Über hypergeometrische funkionen zweier Veränderlichen, Dissertation, Darmstadt
• Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II, McGraw-Hill Book Company, Inc., New York-Toronto-London, MR0058756
• Horn, J. (1935), "Hypergeometrische Funktionen zweier Veränderlichen", Mathematische Annalen, 105 (1): 381–407, doi:10.1007/BF01455825
• J. Horn Math. Ann. 111, 637 (1933)
• Srivastava, H. M.; Karlsson, Per W. (1985), Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-602-7, MR834385