recurrence relation

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recurrence relation

[ri′kər·əns ri‚lā·shən]

(mathematics)

An equation relating a term in a sequence to one or more of its predecessors in the sequence.

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so that the two-term recurrence relation (51) can be rewritten as ([c.sub.0] = 1)

Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

Proof: Upon extending [u.sub.n] to the negative integers using the recurrence relation [u.sub.-4] = [3u.sub.n-2] - [u.sub.n], we note that [u.sub.n] = -[u.sub.-n-2].

Minimum number of colors: the Turk's Head Knots case study

For each fixed m, these two generating functions share the same denominator, hence the same recurrence relation. We used Pascal programs and Mathematica 6 to carry out the computation.

A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs

A recurrence relation for marginal moment generating function for lgos from df (1.5) can be obtained in the following theorem.

Relations for marginal and joint moment generating functions of extended type I generalized logistic distribution based on lower generalized order statistics and characterization

Then method of lines, semidiscritization approach, is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations whose solution satisfies a recurrence relation involving matrix exponential function.

A NUMERICAL TECHNIQUE FOR HEAT EQUATION SUBJECT TO INTEGRAL SPECIFICATIONS

Moreover, combining the annihilation equation and the recursion formula (6) we obtain the following recurrence relation.

Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator

Firstly find the recurrence relation for coefficients and construct with it a program using the calculator to automatically generate coefficients of the series.

Power series solutions of differential equations: programming and experimenting with technology

** The sequence [{[B.sub.n]}.sub.n[greater than or equal to]0] satisfies the three-term recurrence relation

Inverse finite-type relations between sequences of polynomials

It is known that the recurrence relation for incomplete gamma functions {[Lambda] (a + n, x)}, 0 [is less than or equal to] a [is less than] 1, n = 0, 1,2, ..., when x is positive, is unstable--more so the larger x.

A Note on the Recursive Calculation of Incomplete Gamma Functions

Then the recurrence relation (2.25) can be expressed as

THE EXTENDED GLOBAL LANCZOS METHOD FOR MATRIX FUNCTION APPROXIMATION

After studying it carefully, it is found that the solutions cannot be given exactly due to the complicated three-term recurrence relation. The method used by him is nothing but the Bethe ansatz method as summarized in [13].

Exact Solutions of the Razavy Cosine Type Potential

Then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the characteristic polynomial which determines the recurrence relation that [h.sub.m](n) satisfies.