ABSTRACT. In this paper the analogy between the character sum expansion of a complex-valued function over GF(q) and the power series expansion of an analytic function is exploited in order to develop an analogue for hypergeometric series over finite fields. It is shown that such functions satisfy many summation and transformation formulas analogous to their classical counterparts.

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The probability of CKD diagnosis in cats was influenced by several variables; recent weight loss, particularly in combination with the other factors, warrants assessment of cats for CKD.

Rheometric data for short‐fiber‐filled thermoplastics are presented using a parallel‐plate viscometer. Polypropylene tensile bars contain short and long fibers with glass weight percentages of 0%, 5%, 10%, 20%, and 30%, polycarbonate tensile bars with glass percentages of 0%, 5%, and 10% long fibers, and nylon 6/6 tensile bars with 0%, 15%, 30%, and 45% short fibers. The short fibers were initially 3 mm in length and 12.7 microns in diameter. The long fibers were initially 6 mm in length and 10 microns in diameter. In the steady‐state experiments, the fibers increase the viscous stresses and the normal stresses in proportion to the concentration of fibers. At low shear rates, the viscosity is increased by the addition of the fibers, but at high shear rates the viscosity approaches that of the neat resin. In dynamic testing, the fibers increase the viscous and elastic components as measured by the complex viscosity and modulus. The fibers increase the viscous and elastic nature of the fiber‐filled composite at low frequencies and to a lesser extent at higher frequencies. The fibers increase the elastic component more than the viscous component at low frequencies and less at higher frequencies as demonstrated by tan δ.

ABSTRACT. In this paper the analogy between the character sum expansion of a complex-valued function over GF(q) and the power series expansion of an analytic function is exploited in order to develop an analogue for hypergeometric series over finite fields. It is shown that such functions satisfy many summation and transformation formulas analogous to their classical counterparts.