forward recurrence

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1: 5.21 Methods of Computation

… ►Or we can use forward recurrence, with an initial value obtained e. …

2: 3.10 Continued Fractions

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Forward Recurrence Algorithm

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Forward Series Recurrence Algorithm

… ►This forward algorithm achieves efficiency and stability in the computation of the convergents $C_n=A_n/B_n$, and is related to the forward series recurrence algorithm. …

3: 11.13 Methods of Computation

… ►In consequence forward recurrence, backward recurrence, or boundary-value methods may be necessary. …

4: 10.74 Methods of Computation

… ►Then $J_n\left(x\right)$ and $Y_n\left(x\right)$ can be generated by either forward or backward recurrence on $n$ when , but if $n>x$ then to maintain stability $J_n\left(x\right)$ has to be generated by backward recurrence on $n$, and $Y_n\left(x\right)$ has to be generated by forward recurrence on $n$. …

5: 16.25 Methods of Computation

… ►In these cases integration, or recurrence, in either a forward or a backward direction is unstable. …

6: 3.6 Linear Difference Equations

… ►We first compute, by forward recurrence, the solution $p_n$ of the homogeneous equation (3.6.3) with initial values $p_0=0$, $p_1=1$. …

7: 2.9 Difference Equations

… ►Many special functions that depend on parameters satisfy a three-term linear recurrence relation … ►

2.9.2 $${\mathrm{\Delta }}^{2}w(n)+(2+f(n))\mathrm{\Delta }w(n)+(1+f(n)+g(n))w(n)=0,$$ $n=0,1,2,\mathrm{\dots }$,

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Symbols:

$\mathrm{\Delta }$: forward difference operator, $f(n)$: function, $g(n)$: function, $n$: nonnegative integer and $w(n)$: solution

Permalink:

http://dlmf.nist.gov/2.9.E2

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Annotations for §2.9(i), §2.9 and Ch.2

►in which $\mathrm{\Delta }$ is the forward difference operator (§3.6(i)). …

8: 18.2 General Orthogonal Polynomials

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§18.2(iv) Recurrence Relations

… ►the monic recurrence relations (18.2.8) and (18.2.10) take the form … ►Then, with the coefficients (18.2.11_4) associated with the monic OP’s $p_n$, the orthonormal recurrence relation for $q_n$ takes the form … ►The recurrence relations (18.2.10) can be equivalently written as … ►More generally, §18.30 defines the recurrence relation of the $c$th associated monic OP by means of a similar shift by $c$ in (18.2.11_5). …