Live briefing
Everything about Polynomial sequence
Sequence valued in polynomials
In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics, as well as applied mathematics. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Polynomial sequenceA 5-minute orientation
- Skim a recent paper: Structural impact of the start-up sequence on Pelton turbines lifetime: Analytical prediction and polynomial optimizationInfluential work since 2022
- Pick up a classic book: Walsh equiconvergence of complex interpolating polynomialsThe most-reprinted book on the subject
- Read the landmark paper: Generalized Lucas polynomial sequence approach for fractional differential equationsCited 83 times
- Go sideways: Umbral calculusA closely related topic
- Go sideways: Sheffer sequenceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Generalized Lucas polynomial sequence approach for fractional differential equations
A Polynomial Time Solvable Formulation of Multiple Sequence Alignment
An efficient polynomial space and polynomial delay algorithm for enumeration of maximal motifs in a sequence
A generalization of Lucas polynomial sequence
Generalized Lucas Polynomial Sequence Treatment of Fractional Pantograph Differential Equation
A POLYNOMIAL ANALOGUE TO THE STERN SEQUENCE
Polynomial remainder sequence and approximate GCD
Convergence acceleration of polynomial chaos solutions via sequence transformation
🆕 Influential since 2022
Structural impact of the start-up sequence on Pelton turbines lifetime: Analytical prediction and polynomial optimization
The parabolic mean operator and related polynomial sequence: a theoretical approach
UNIPOL: Unimodular sequence design via a separable iterative quartic polynomial optimization for active sensing systems
Collocation Method for the Time-Fractional Generalized Kawahara Equation Using a Certain Lucas Polynomial Sequence
A Low Complexity and Long Period Digital Random Sequence Generator Based on Residue Number System and Permutation Polynomial
📚 Books worth reading
Walsh equiconvergence of complex interpolating polynomialsAmnon Jakimovski · 2006
Polynomial Root-finding and PolynomiographyBahman Kalantari · 2008
Sage for undergraduatesGregory V. Bard · 2015
The ultimate challengeJeffrey C. Lagarias · 2010- 📕Sopra lo sviluppo della funzione [1 over ce¹⁰-1], e sopra una nuova espressione dei numeri di BernoulliE. Fergola · 1860
- 📕Sopra lo sviluppo della funzione [1 over ce℗£ʻ́-1], e sopra una nuova espressione dei numeri di BernoulliE. Fergola · 1860
- 📕Polynomials of convolution typeAlessandro Di Bucchianico · 1991
Use of sequential differences in smoothing 3-D dataJoseph Bryce Tysver · 1979
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Umbral calculus The term umbral calculus has two related but distinct meanings. In mathematics, before the 1970s, umbral calculus referred to the surprising similarity…
- Sheffer sequence In mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence ( pn(x) : n = 0, 1, 2, 3, ... ) of polynomials in which the index…
- Binomial type In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers {0,1,2,3,…} in which the index of each polynomial…
- Falling and rising factorials In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial…
- Outline of combinatorics Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Matroid Greedoid Ramsey theory Van der Waerden's…
- Lah number In mathematics, the (signed and unsigned) Lah numbers are coefficients expressing rising factorials in terms of falling factorials and vice versa. They…
- Abel polynomials The Abel polynomials are a sequence of polynomials named after Niels Henrik Abel, defined by the following equation: pn(x)=x(x−an)n−1 They occur, for instance…
- Orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to…