Live briefing
Everything about Recurrence relation
Pattern defining an infinite sequence of numbers
In mathematics, a recurrence relation is an equation according to which the th term of a sequence is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation. If the values of the first numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Recurrence relationA 5-minute orientation
- Skim a recent paper: Socioeconomic status and its relation with breast cancer recurrence and survival in young women in the NetherlandsInfluential work since 2022
- Pick up a classic book: Traumatic RupturesThe most-reprinted book on the subject
- Read the landmark paper: Fourth Order Chebyshev Methods with Recurrence RelationCited 138 times
- Go sideways: Linear recurrence with constant coefficientsA closely related topic
- Go sideways: P-recursive equationA closely related topic
📖 Definitions
Noun an equation that recursively defines a sequence; each term of the sequence is defined as a function of the preceding terms.
🏆 Landmark papers (most cited)
Fourth Order Chebyshev Methods with Recurrence Relation
A recurrence relation for chebyshevianB-splines
Magnitude-recurrence relation for central Mississippi Valley earthquakes
A recurrence relation for inclination functions
Orthogonal polynomials defined by a recurrence relation
Generalization of Spivey’s Recurrence Relation
A GENERALIZED EMERSON RECURRENCE RELATION
A recurrence relation for the βn-function
🆕 Influential since 2022
Socioeconomic status and its relation with breast cancer recurrence and survival in young women in the Netherlands
Time to recurrence and its relation to survival after recurrence in patients resected for stage III colon cancer
Exploring phenotypes of deep vein thrombosis in relation to clinical outcomes beyond recurrence
SQSTM1 Expression in Hepatocellular Carcinoma and Relation to Tumor Recurrence After Radiofrequency Ablation
Mammographic density in relation to breast cancer recurrence and survival in women receiving neoadjuvant chemotherapy
📚 Books worth reading
Traumatic RupturesRobin A. Deutsch · 2014
Cue extinctionPeter McCahill · 1993
Advanced combinatoricsLouis Comtet · 1974
Mistaken beliefs about relapseTerence T. Gorski, Merlene Miller · 1988
Relapse and recovery in addictionsCarl G Leukefeld · 2001
Safe medicine for sober peopleJeffrey Weisberg, Gene Hawes · 2005
Therapist's guide to evidence-based relapse preventionG. Alan Marlatt · 2007
Mindfulness-based relapse prevention for addictive behaviorsSarah Bowen · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Linear recurrence with constant coefficients In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear…
- P-recursive equation In mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive…
- Linear differential equation In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written…
- Finite difference A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often…
- Three-term recurrence relation In mathematics, and especially in numerical analysis, a homogeneous linear three-term recurrence relation (TTRR, the qualifiers "homogeneous linear" are…
- Holonomic function In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear…
- Chebyshev polynomials The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, denoted as Tn(x) and Un(x). They can be…
- Laguerre polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: xy″+(1−x)y′+ny=…