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 π‘Ž 𝑛 subscript 𝑀 𝑛 1 subscript 𝑏 𝑛 subscript 𝑀 𝑛 subscript 𝑐 𝑛 subscript 𝑀 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
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3.6.E5 βˆ‘ n = 0 ∞ Ξ» n ⁒ w n = 1 superscript subscript 𝑛 0 subscript πœ† 𝑛 subscript 𝑀 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
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3.6.E10 p n + 1 ⁒ w n = p n ⁒ w n + 1 + e n subscript 𝑝 𝑛 1 subscript 𝑀 𝑛 subscript 𝑝 𝑛 subscript 𝑀 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]
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3.6.E11 w n + 1 - 2 ⁒ n ⁒ w n + w n - 1 = 0 subscript 𝑀 𝑛 1 2 𝑛 subscript 𝑀 𝑛 subscript 𝑀 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
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3.6.E14 w n + 1 - 2 ⁒ n ⁒ w n + w n - 1 = - ( 2 / Ο€ ) ⁒ ( 1 - ( - 1 ) n ) subscript 𝑀 𝑛 1 2 𝑛 subscript 𝑀 𝑛 subscript 𝑀 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]
Failed [300 / 300]
3.6.E17 a n ⁒ w n + 1 - b n ⁒ w n = d n subscript π‘Ž 𝑛 subscript 𝑀 𝑛 1 subscript 𝑏 𝑛 subscript 𝑀 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]
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