Properties of generalized univariate hypergeometric functions

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E_7 (elliptic, hyperbolic) and of type E_6 (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars' relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.Comment: 46 page

Laminitis in dairy goats (Capra aegagrus hircus) on a low-forage diet

Dairy goats on high-concentrate diets attain high production levels, but at what cost? Here, ongoing lameness problems in a herd offered ad lib concentrates and roughages throughout their lifetime were investigated. Five severely affected, chronically lame animals were euthanased and examined postmortem. Foot pathology consisted of distortion of the claw shape and irregular fissures over the solar and bulbar horn with the distal phalanx rotated downwards on two claws. Rumen pH was measured between 5.26 and 5.46 with moderate rumen mucosa hyperkeratosis, and ulcerative, mild lymphocytic rumenitis. Feet showed irregular hyperplasia of the epidermal laminae with parakeratotic hyperkeratosis, especially in solar regions. Dense clusters of lymphocytes expanded the dermal laminae. Based on these findings, chronic laminitis was suspected. Ruminal hyperkeratosis was likely a result of prolonged periods of acidosis. The consequences of feeding a high-concentrate ration throughout the life of dairy goats need more research