Horn function

In the theory of special functions in mathematics, the Horn functions (named for Jacob Horn) are the 34 distinct convergent hypergeometric series of order two (i.e. having two independent variables), enumerated by Horn (1931) (corrected by Borngässer (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, http://apps.nrbook.com/bateman/Vol2.pdf 
• Horn, J. (1935), "Hypergeometrische Funktionen zweier Veränderlichen", Mathematische Annalen 105 (1): 381–407, doi:10.1007/BF01455825, http://www.digizeitschriften.de/main/dms/img/?IDDOC=364781 
• 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