Results 121 to 130 of about 1,148,545 (158)

Binet's formula for generalized tribonacci numbers

International Journal of Mathematical Education in Science and Technology, 2015
In this note, we derive Binet's formula for the general term Tn of the generalized tribonacci sequence. This formula gives Tn explicitly as a function of the index n, the roots of the associated characteristic equation, and the initial terms T0, T1, and T2.
J. Cereceda
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A New Generalization of Fibonacci Sequence & Extended Binet's Formula

Integers, 2009
AbstractConsider the Fibonacci ...
Edson, Marcia, Yayenie, Omer
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Generalization of Binet's Gamma function formulas

Integral Transforms and Special Functions, 2013
Several representations for the logarithm of the Gamma function exist in the literature. There are four important expansions which bear the name of Binet. Hermite generalized Binet's first formula to the logarithm of the Gamma function with shifted argument.
G. Nemes
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Binet’s Formula for the Recursive Sequence of Order K

The Fibonacci Quarterly, 1984
The terms of a recursive sequence are usually defined by a recurrence procedure; that is, any term is the sum of preceding terms. Such a definition might not be entirely satisfactory, because the computation of any term could require the computation of ...
W. R. Spickerman, R. N. Joyner
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Binet’s Formula Generalized

The Fibonacci Quarterly, 1977
A. Whitford
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Leonardo Cartan Numbers and Related Fibonacci–Lucas Structures

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper investigates the Leonardo Cartan numbers, defined as an extension of the classical Leonardo sequence through additional algebraic structures. The recurrence relations of these numbers are established, and various summation formulas are derived.
Hasan Çakır, İskender Öztürk
semanticscholar   +2 more sources

A Generalization of Binet’s Formula and Some of Its Consequences

The Fibonacci Quarterly, 1989
Darío Castellanos
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Some New Representations of the Binet's Function Involving Euler Sums

American Review of Mathematics and Statistics, 2022
We consider a method for transforming divergent series arising from the Euler - Maclaurin formula into convergent ones. Applying it to the Stirling series forlog 𝛤(𝑧)we obtain some new representations of the J. Binet function.
N. Naĭdenov
semanticscholar   +1 more source

Stirling’s Original Asymptotic Series from a Formula Like One of Binet’s and its Evaluation by Sequence Acceleration

Experimental Mathematics, 2018
We give an apparently new proof of Stirling’s original asymptotic formula for the behavior of for large z. Stirling’s original formula is not the formula widely known as “Stirling’s formula”, which was actually due to De Moivre.
Robert M Corless, Leili Rafiee Sevyeri
semanticscholar   +1 more source

Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Qi, Bai-Ni Guo
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