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34 lines
685 B
34 lines
685 B
#!/usr/local/bin/bc -l |
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### SRR.BC - Sum of Repeated Roots (less one); |
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### calculate the value of sum[n=1..oo] x^(2^(-n))-1 |
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define srr(x) { |
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auto s,t,os; |
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if(x<=0){print "srr: Negative Infinity\n";return 1-A^scale} |
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scale+=6 |
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s=x ; os=s+1 |
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t=0;while(os!=s){ |
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os=s |
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s=sqrt(s) |
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t+=s-1 |
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} |
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scale-=6;t/=1 |
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return(t); |
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} |
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define srr_n(n,x) { # Generalisation of srr; srr(x) == srr_n(2,x) |
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auto s,t,os; |
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if(x<=0){print "srr_n: Negative Infinity\n";return 1-A^scale} |
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if(n==2)return(srr(x)) |
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if(n<=1){print "srr_n: Infinity\n";return A^scale-1} |
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scale+=6 |
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s=x ; os=s+1 |
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t=0;while(os!=s){ |
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os=s |
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s=e(l(s)/n) |
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t+=s-1 |
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} |
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scale-=6;t/=1 |
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return(t); |
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}
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