Results 161 to 170 of about 13,300 (186)

On a generalized Appell system and monogenic power series

Mathematical Methods in the Applied Sciences, 2009
AbstractRecently Appell systems of monogenic polynomials in ℝ3were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion‐valued functions. A new Taylor‐type series expansion based on the Appell polynomials is presented, which can be related to
S. Bock, Klaus Gürlebeck
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A family of algebraic curves and Appell series over finite fields

The Ramanujan Journal
The authors establish a relation between the number of points on the nonsingular projective curve \(C_{a,b,c,d,e}\) over \(\mathbb{Q}\), given by the affine equation \(ax^2 + by^2 = c + dx y + ex^2 y^2\), and the finite field Appell series \(F_{4}^{*}\).
Shaik Azharuddin, Gautam Kalita
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Transformations for Appell series over finite fields and traces of Frobenius for elliptic curves

Finite Fields and Their Applications, 2023
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Gautam Kalita, Shaik Azharuddin
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F4-Appell series in p-adic settings and their connections to algebraic curves

Journal of Mathematical Analysis and Applications
The finite field Appell series enjoy many summation, reduction, product, and transformation formulas analogous to their classical counterparts. Relating finite field Appell series and Gaussian hypergeometric series has led mathematicians to investigate possible connections between finite field Appell series and algebraic curves as well as other number ...
Shaik Azharuddin, Gautam Kalita
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Traces of Frobenius for elliptic curves and Appell series in p -adic settings

International Journal of Number Theory
Let [Formula: see text] be an odd prime and [Formula: see text] denote the finite field with [Formula: see text] elements. In this paper, we express the trace of Frobenius of a family of elliptic curves in terms of [Formula: see text] Appell series over [Formula: see text] under certain restrictions on [Formula: see text].
Shaik Azharuddin, Gautam Kalita
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q-supercongruences for truncated q-Appell series

Advances in Applied Mathematics
Haihong He, Xiaoxia Wang
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On some infinite series involving appell-polynomials and the functions F(z,α)—I

Proceedings of the Indian Academy of Sciences - Section A, 1964
S.K. Rangarajan
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Appell’s hypergeometric series over finite fields

International Journal of Number Theory, 2019
We define four functions [Formula: see text] and [Formula: see text] as finite field analogues of Appell series [Formula: see text] and [Formula: see text], respectively using purely Gauss sums in the spirit of finite field hypergeometric series introduced by McCarthy.
Tripathi, Mohit, Saikia, Neelam, Barman, Rupam   +2 more
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Elliptic curves and Appell series over finite fields

Journal of Mathematical Analysis and Applications
S. K. Maity, Rupam Barman
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A finite field analogue of the Appell series $$F_4$$ F 4

Research in Number Theory, 2018
Mohit Tripathi, Rupam Barman
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