Horn Function
المؤلف:
Borngässer, L.
المصدر:
Über hypergeometrische Funktionen zweier Veränderlichen. Dissertation. Darmstadt, Germany: University of Darmstadt, 1933.
الجزء والصفحة:
...
15-6-2019
2074
Horn Function
The 34 distinct convergent hypergeometric series of order two enumerated by Horn (1931) and corrected by Borngässer (1933). There are 14 complete series for which 
:
(of which 
, 
, 
, and 
are precisely Appell hypergeometric functions), and 20 confluent series with 
, 
, and 
not both 2:
(Erdélyi et al. 1981, pp. 224-226; Srivastava and Karlsson 1985, pp. 24-26). Here, the sums are taken over nonnegative integers 
and 
.
Note that 
, 
, and 
as defined by Erdélyi et al. (1981) are erroneous; the correct formulas given above may be found in Srivastava and Karlsson (1985, pp. 25-26).
REFERENCES:
Borngässer, L. Über hypergeometrische Funktionen zweier Veränderlichen. Dissertation. Darmstadt, Germany: University of Darmstadt, 1933.
Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. "Horn's List" and "Convergence of the Series." §5.7.1 and 5.7.2 in Higher Transcendental Functions, Vol. 1. New York: Krieger, pp. 224-229, 1981.
Horn, J. "Hypergeometrische Funktionen zweier Veränderlichen." Math. Ann. 105, 381-407, 1931.
Srivastava, H. M. and Karlsson, P. W. Multiple Gaussian Hypergeometric Series. Chichester, England: Ellis Horwood, 1985.
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