A note on generating functions and summation formulae for Meixner polynomials of several variables
Abstract The present paper deals with certain generating functions and various elegant summation formulae for Meixner polynomials of several variables.
Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polynomials is presented. It is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. The weight function associated with the Krawtchouk polynomials is the multivariate binomial distribution.
Cytoplsmic uridine phosphorylase of rat liver. Characterization and kinetics.
Abstract Uridine phosphorylase (uridine:orthophosphate ribosyltransferase, EC 2.4.2.3) of rat liver cytoplasm has been purified 1900-fold. Initial velocity patterns of the phosphorolysis of uridine or deoxyuridine and of the synthesis of uridine indicated a sequential mechanism. Product inhibition patterns with uracil or ribose 1-phosphate as inhibitors were consistent with an "ordered Bi Bi" reaction in which inorganic phosphate is the first substrate to bind to the enzyme and ribose 1-phosphate the last product to leave the enzyme. The most highly purified enzyme fractions still retained uridine-, deoxyuridine-, and thymidine-cleaving activities in the ratio of 10:7:1 at pH 7.4. The fractions separated into a major and a minor band of protein on electrophoresis in phosphate buffer. Aging of the enzyme with loss of activity resulted in an increase in the proportion of the minor band. The pH optimum of the enzyme for uridine cleavage was 8.2, for deoxyuridine cleavage, 6.5, and for uridine synthesis, 8.5. Uridine or deoxyuridine synthesis was inhibited 50% in the presence of 1 mm uracil. The enzyme did not catalyze the direct transfer of ribose from uridine to uracil in the absence of phosphate. Uridine protected the enzyme to a greater degree than phosphate against inhibition by o-iodosobenzoate. Thus, at least one sulfhydryl group and possibly three are present at or near the active site. Uridine cleavage, uridine synthesis, and deoxyuridine cleavage were inhibited by deoxyglucosylthymine. The phosphorolysis of deoxyuridine and thymidine by thymidine phosphorylase, also purified from rat liver cytoplasm, was not inhibited by deoxyglucosylthymine. The molecular weights of both uridine and thymidine phosphorylases were estimated to be 110,000.