Numerical Methods - 3.6 Linear Difference Equations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
3.6.E3 a n ⁢ w n + 1 - b n ⁢ w n + c n ⁢ w n - 1 = 0 subscript 𝑎 𝑛 subscript 𝑤 𝑛 1 subscript 𝑏 𝑛 subscript 𝑤 𝑛 subscript 𝑐 𝑛 subscript 𝑤 𝑛 1 0 {\displaystyle{\displaystyle a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1}=0}}
a_{n}w_{n+1}-b_{n}w_{n}+c_{n}w_{n-1} = 0		 

a[n]*w[n + 1]- b[n]*w[n]+ c[n]*w[n - 1] = 0
 
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n]+ Subscript[c, n]*Subscript[w, n - 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
3.6.E5 ∑ n = 0 ∞ λ n ⁢ w n = 1 superscript subscript 𝑛 0 subscript 𝜆 𝑛 subscript 𝑤 𝑛 1 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\lambda_{n}w_{n}=1}}
\sum_{n=0}^{\infty}\lambda_{n}w_{n} = 1		 

sum(lambda[n]*w[n], n = 0..infinity) = 1
 
Sum[Subscript[\[Lambda], n]*Subscript[w, n], {n, 0, Infinity}, GenerateConditions->None] == 1
 Skipped - no semantic math Skipped - no semantic math - -
3.6.E10 p n + 1 ⁢ w n = p n ⁢ w n + 1 + e n subscript 𝑝 𝑛 1 subscript 𝑤 𝑛 subscript 𝑝 𝑛 subscript 𝑤 𝑛 1 subscript 𝑒 𝑛 {\displaystyle{\displaystyle p_{n+1}w_{n}=p_{n}w_{n+1}+e_{n}}}
p_{n+1}w_{n} = p_{n}w_{n+1}+e_{n}		 

p[n + 1]*w[n] = p[n]*w[n + 1]+ exp(1)[n]
 
Subscript[p, n + 1]*Subscript[w, n] == Subscript[p, n]*Subscript[w, n + 1]+ Subscript[E, n]
 Skipped - no semantic math Skipped - no semantic math - -
3.6.E11 w n + 1 - 2 ⁢ n ⁢ w n + w n - 1 = 0 subscript 𝑤 𝑛 1 2 𝑛 subscript 𝑤 𝑛 subscript 𝑤 𝑛 1 0 {\displaystyle{\displaystyle w_{n+1}-2nw_{n}+w_{n-1}=0}}
w_{n+1}-2nw_{n}+w_{n-1} = 0		 

w[n + 1]- 2*n*w[n]+ w[n - 1] = 0
 
Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == 0
 Skipped - no semantic math Skipped - no semantic math - -
3.6.E14 w n + 1 - 2 ⁢ n ⁢ w n + w n - 1 = - ( 2 / π ) ⁢ ( 1 - ( - 1 ) n ) subscript 𝑤 𝑛 1 2 𝑛 subscript 𝑤 𝑛 subscript 𝑤 𝑛 1 2 1 superscript 1 𝑛 {\displaystyle{\displaystyle w_{n+1}-2nw_{n}+w_{n-1}=-(2/\pi)(1-(-1)^{n})}}
w_{n+1}-2nw_{n}+w_{n-1} = -(2/\cpi)(1-(-1)^{n})		 

w[n + 1]- 2*n*w[n]+ w[n - 1] = -(2/Pi)*(1 -(- 1)^(n))

Subscript[w, n + 1]- 2*n*Subscript[w, n]+ Subscript[w, n - 1] == -(2/Pi)*(1 -(- 1)^(n))
Failure Failure
Failed [300 / 300]
Result: 1.273239544+0.*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: -1.732050808-1.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}


Result: -2.190862072-2.000000000*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = 1/2*3^(1/2)+1/2*I, n = 3}


Result: -.927858596e-1+.3660254040*I
Test Values: {w[n] = 1/2*3^(1/2)+1/2*I, w[n-1] = 1/2*3^(1/2)+1/2*I, w[n+1] = -1/2+1/2*I*3^(1/2), n = 1}

... skip entries to safe data
Failed [300 / 300]
Result: 1.2732395447351628
Test Values: {Rule[n, 1], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-1.7320508075688774, -0.9999999999999999]
Test Values: {Rule[n, 2], Rule[Subscript[w, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
3.6.E17 a n ⁢ w n + 1 - b n ⁢ w n = d n subscript 𝑎 𝑛 subscript 𝑤 𝑛 1 subscript 𝑏 𝑛 subscript 𝑤 𝑛 subscript 𝑑 𝑛 {\displaystyle{\displaystyle a_{n}w_{n+1}-b_{n}w_{n}=d_{n}}}
a_{n}w_{n+1}-b_{n}w_{n} = d_{n}		 

a[n]*w[n + 1]- b[n]*w[n] = d[n]
 
Subscript[a, n]*Subscript[w, n + 1]- Subscript[b, n]*Subscript[w, n] == Subscript[d, n]
 Skipped - no semantic math Skipped - no semantic math - -
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