Horn function

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In the theory of special functions in mathematics, the Horn functions (named for Jakob 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). B. C. Carlson[1] revealed a problem with the Horn function classification scheme.[2]


  1. ^ 'Profile: Bille C. Carlson' in Digital Library of Mathematical Functions. National Institute of Standards and Technology.
  2. ^ Carlson, B. C. (1976). "The need for a new classification of double hypergeometric series". Proc. Amer. Math. Soc. 56: 221–224. MR 0402138. doi:10.1090/s0002-9939-1976-0402138-8.