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Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)

Atsuhira Nagano (2015)

Acta Arithmetica

The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for ℚ (√5). We study a family of Kummer surfaces corresponding to the Humbert surface of invariant 5 with two complex parameters. Our Kummer surface is given by a double covering of the weighted projective space ℙ(1:1:2) branched along a parabola and a quintic curve. The period mapping for our family is given by double integrals of an algebraic function on chambers coming from an arrangement...

Drought models based on Burr XII variables

Saralees Nadarajah, B. M. Golam Kibria (2006)

Applicationes Mathematicae

Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.

Duplicate inverse series relations and hypergeometric evaluations with z = 1 / 4

Wenchang Chu (2002)

Bollettino dell'Unione Matematica Italiana

The Gould-Hsu (1973) inverse series relations have been systematically applied to the research of hypergeometric identities. Their duplicate version is established and used to demonstrate several terminating F 2 3 ⁢ 1 / 4 -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.

E -orbit functions.

Klimyk, Anatoliy U., Patera, Jiri (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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