Explicitly, recurrence yields the equations:

Subtracting the original recurrence from this equation yields

Beal suggests using the above recurrence to shift x to a value greater than 6 and then applying the above expansion with terms above cut off, which yields " more than enough precision ".

According to Ord, Pearson devised the underlying form of Equation ( 1 ) on the basis of, firstly, the formula for the derivative of the logarithm of the density function of the normal distribution ( which gives a linear function ) and, secondly, from a recurrence relation for values in the probability mass function of the hypergeometric distribution ( which yields the linear-divided-by-quadratic structure ).

A multistep method appled to this differential equation with step size h yields a linear recurrence relation with characteristic polynomial

This yields a convenient way of generating an equivalence relation: given any binary relation R on X, the equivalence relation generated by R is the smallest equivalence relation containing R. Concretely, R generates the equivalence relation a ~ b if and only if there exist elements x < sub > 1 </ sub >, x < sub > 2 </ sub >, ..., x < sub > n </ sub > in X such that a

Rearranging to express the relation between standard potential and equilibrium constant yields

Configurations and the yields relation on configurations, which describes the possible actions of the Turing machine given any possible contents of the tape, are as for standard Turing machines, except that the yields relation is no longer single-valued.

It is possible to derive, from the covariant formulation of full quantum theory ( Spinfoam ) the correct relation between energy and area ( 1st law ), the Unruh temperature and the distribution that yields Hawking entropy.

It is possible to derive, from the covariant formulation of full quantum theory ( Spinfoam ) the correct relation between energy and area ( 1st law ), the Unruh temperature and the distribution that yields Hawking entropy.

Comparing these two yields the relation above.

A basic understanding of the terminology of cleavage energy, surface energy, and surface tension is very helpful for understanding the physical state and the events that happen at a given surface, but as discussed below, the theory of these variables also yields some interesting effects that concern the practicality of adhesive surfaces in relation to their surroundings.

When yields are periodically-compounded Macaulay and modified duration will differ slightly, and in this case there is a simple relation between the two.

The ideal Ohm's law then yields the relation

Multiplying the ( n-1 ) th triangular number by 9 and then adding 1 yields the nth centered nonagonal number, but centered nonagonal numbers have an even simpler relation to triangular numbers: every third triangular number ( the 1st, 4th, 7th, etc.

Alley cropping has been shown to be advantagous in Africa, particularly in relation to improving maize yields in the sub-Saharan region.

Then S is a predecessor of T, in symbols, if for each, every path connecting x to b meets T. It follows from the definition that the predecessor relation yields a preorder on the set of all ( a, b )- separators.

In this case the relation reads b < sup > 2 </ sup > = a < sup > 2 </ sup > + ab which yields the golden ratio

But and are congruent modulo, and so each such integer z that we find yields a multiplicative relation ( mod n ) among the elements of P, i. e.

For such an online algorithm, a recurrence relation is required between quantities from which the required statistics can be calculated in a numerically stable fashion.

The recurrence relation reads

:* Escape-time fractals – use a formula or recurrence relation at each point in a space ( such as the complex plane ); usually quasi-self-similar ; also known as " orbit " fractals ; e. g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal.

In mathematical terms, the sequence F < sub > n </ sub > of Fibonacci numbers is defined by the recurrence relation

The logistic map is a polynomial mapping ( equivalently, recurrence relation ) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations.

The generator is defined by the recurrence relation:

The Fibonacci sequence may be described by the recurrence relation:

A discrete function could be defined explicitly by a list, or by a formula for f ( n ) or it could be given implicitly by a recurrence relation or difference equation.

And rearranging terms gives the recurrence relation

The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output.

And rearranging terms gives the recurrence relation

The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output.

and the recurrence relation

For non-zero b and positive n, the recurrence relation from the previous subsection can be rewritten as

A nonlinear recurrence relation defines successive terms of a sequence as a nonlinear function of preceding terms.

In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms.

The term difference equation sometimes ( and for the purposes of this article ) refers to a specific type of recurrence relation.

However, " difference equation " is frequently used to refer to any recurrence relation.

An example of a recurrence relation is the logistic map:

Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n.

The Fibonacci numbers are the archetype of a linear, homogeneous recurrence relation with constant coefficients ( see below ).

They are defined using the linear recurrence relation

An order d linear homogeneous recurrence relation with constant coefficients is an equation of the form

A sequence which satisfies a relation of this form is called a linear recurrence sequence or LRS.

More generally, given the recurrence relation: