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Adam Ledger

Mr. Adam Ledger

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8 years, 288 days
unemployed
hobo
Perth, Australia

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These are Posts that have been published by Adam Ledger

odd Zeta value series approximation to t...

Adam Ledger 360 Maple
constants exponential
August 18 2016
-1 0


> 

(41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2+sqrt(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4))*(41403013072+527237505*Zeta(5)^2-sqrt(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4))/((41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2-sqrt(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4))*(41403013072+527237505*Zeta(5)^2+sqrt(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4)))-3/7-(1/10)*(exp(Pi)+5)/(Ei(1)+1/2)

(41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2+(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))*(41403013072+527237505*Zeta(5)^2-(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))/((41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2-(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))*(41403013072+527237505*Zeta(5)^2+(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2)))-3/7-(1/10)*(exp(Pi)+5)/(Ei(1)+1/2)

 (1)
> 

abs(evalf[1000]((41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2+(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))*(41403013072+527237505*Zeta(5)^2-(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))/((41403013072+527237505*Zeta(3)^2+8631147672*Zeta(3)+527237505*Zeta(5)^2-(1714209491440202877184+118155152758998350304*Zeta(3)^2+714711039780356736768*Zeta(3)+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(3)^4+9101329527743676720*Zeta(3)^3+555958773357250050*Zeta(3)^2*Zeta(5)^2+9101329527743676720*Zeta(3)*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2))*(41403013072+527237505*Zeta(5)^2+(1714209491440202877184+30838267512743688864*Zeta(5)^2+277979386678625025*Zeta(5)^4)^(1/2)))-3/7-(1/10)*(exp(Pi)+5)/(Ei(1)+1/2)))

0.4022755651e-7

 (2)
> 

``


Download EXPONENTIAL_INTEGRAL_ODD_ZETA_SERIES_APPROXIMATION.mw

CONGRUENT FUNCTIONS OF THE FRACTIONAL ...

Adam Ledger 360 Maple
August 17 2016
0 1

A more honest and specific version of lemma 3.

CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw .

Download CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_4.mw

Prime number subset code using set and l...

Adam Ledger 360 Maple
prime subset
August 02 2016
1 26

hello i was just looking back on some stuff i did a few months back and although im aware there is a function for generating the prime subset up to a given number already featured in a package in mape im just curious to know how this one measures up in terms of computational efficiency etc.

 

anyway, this is code, if anyone has the time to give it a try and let me know what they think ie faster more logical way about it any feed back is appreciated cheers.

 

restart;
interface(showassumed = 0, rtablesize = infinity);
with(plots); with(numtheory); with(Statistics); with(LinearAlgebra); with(RandomTools); with(codegen, makeproc); with(combinat); with(Maplets[Elements]);
unprotect(real, rational, integer, complex);
alias(P[In] = CurveFitting[PolynomialInterpolation]); alias(L[In] = CurveFitting[LeastSquares]); alias(R[In] = CurveFitting[RationalInterpolation]); alias(S[In] = CurveFitting[Spline]); alias(B[In] = CurveFitting[BSplineCurve]); alias(L[In] = CurveFitting[ThieleInterpolation], rho = frac); alias(`𝒩` = Count); alias(`𝔻` = numtheory:-divisors); alias(sigma = numtheory:-sigma); alias(`ℱ` = ListTools['Flatten']); alias(`𝕊` = seq);
delta := proc (x, y) options operator, arrow; piecewise(x = y, 1, x <> y, 0) end proc;
`&Mopf;` := proc (X, Y) options operator, arrow; map(X, Y) end proc;
`&Cscr;`[S, L] := proc (X) options operator, arrow; convert(X, 'list') end proc;
`&Cscr;`[L, S] := proc (X) options operator, arrow; convert(X, 'set') end proc;
`&Popf;` := proc (N) options operator, arrow; `minus`({`&Sopf;`(k*delta(`&Nscr;`(`&Fscr;`(`&Cscr;`[S, L](`&Mopf;`(`&Cscr;`[S, L], `&Mopf;`(`&Dopf;`, `&Dopf;`(k)))))), 3), k = 1 .. N)}, {0}) end proc;
N -> `minus`({(k delta(&Nscr;(&Fscr;(&Cscr;[S, L]((&Cscr;[S, L])

  &Mopf; (&Dopf; &Mopf; (&Dopf;(k)))))), 3)) &Sopf; (k = 1 .. N)},

  {0})
n[P] := proc (N) options operator, arrow; `&Nscr;`(`&Cscr;`[S, L](`&Popf;`(N)))-1 end proc;



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/prime_subset_up_to_N.mw .

Download prime_subset_up_to_N.mw

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