A better closed-form solution to recursive equation

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Is there a way to represent
beginequation
M(n)=-2times |M(n-1)-0.5|+1
endequation



in closed-form without using the $min$ function? i.e. not:



beginequation
M(n)=2timesminbig2^n-1M(1)-lfloor2^n-1M(1)rfloor,lfloor2^n-1M(1)+1rfloor-2^n-1M(1)big
endequation



where $ 0 leq M(1)leq 1$




sequences-and-series algorithms recurrence-relations closed-form recursion




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  • Is $M$ a function $mathbb N to mathbb R$ ?
    – DanielV
    Jul 16 at 1:53










  • @DanielV M is any real number from 0 to 1
    – RoryHector
    Jul 17 at 15:07














up vote
1
down vote

favorite
2












Is there a way to represent
beginequation
M(n)=-2times |M(n-1)-0.5|+1
endequation



in closed-form without using the $min$ function? i.e. not:



beginequation
M(n)=2timesminbig2^n-1M(1)-lfloor2^n-1M(1)rfloor,lfloor2^n-1M(1)+1rfloor-2^n-1M(1)big
endequation



where $ 0 leq M(1)leq 1$




sequences-and-series algorithms recurrence-relations closed-form recursion




share|cite|improve this question





















  • Is $M$ a function $mathbb N to mathbb R$ ?
    – DanielV
    Jul 16 at 1:53










  • @DanielV M is any real number from 0 to 1
    – RoryHector
    Jul 17 at 15:07












up vote
1
down vote

favorite
2









up vote
1
down vote

favorite
2






2





Is there a way to represent
beginequation
M(n)=-2times |M(n-1)-0.5|+1
endequation



in closed-form without using the $min$ function? i.e. not:



beginequation
M(n)=2timesminbig2^n-1M(1)-lfloor2^n-1M(1)rfloor,lfloor2^n-1M(1)+1rfloor-2^n-1M(1)big
endequation



where $ 0 leq M(1)leq 1$




sequences-and-series algorithms recurrence-relations closed-form recursion




share|cite|improve this question













Is there a way to represent
beginequation
M(n)=-2times |M(n-1)-0.5|+1
endequation



in closed-form without using the $min$ function? i.e. not:



beginequation
M(n)=2timesminbig2^n-1M(1)-lfloor2^n-1M(1)rfloor,lfloor2^n-1M(1)+1rfloor-2^n-1M(1)big
endequation



where $ 0 leq M(1)leq 1$





sequences-and-series algorithms recurrence-relations closed-form recursion





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 16 at 9:06
























asked Jul 15 at 21:17









RoryHector

9012




9012











  • Is $M$ a function $mathbb N to mathbb R$ ?
    – DanielV
    Jul 16 at 1:53










  • @DanielV M is any real number from 0 to 1
    – RoryHector
    Jul 17 at 15:07
















  • Is $M$ a function $mathbb N to mathbb R$ ?
    – DanielV
    Jul 16 at 1:53










  • @DanielV M is any real number from 0 to 1
    – RoryHector
    Jul 17 at 15:07















Is $M$ a function $mathbb N to mathbb R$ ?
– DanielV
Jul 16 at 1:53




Is $M$ a function $mathbb N to mathbb R$ ?
– DanielV
Jul 16 at 1:53












@DanielV M is any real number from 0 to 1
– RoryHector
Jul 17 at 15:07




@DanielV M is any real number from 0 to 1
– RoryHector
Jul 17 at 15:07















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