Aunemco.txt

// Aunemco.txt is the C++ code generated with Mathematica for evaluation of coefficients of the asymptoric expansion of function AuNem at small values of the argument (and positive values of the real part of the argument). These coefficients are used for evaluation of function AuNem.

// Q has sense of parameter of the Nemtsov function; K=Q^2

// In some programs, these Q and K are defined as global variables.

C[1]=(0.5 - K)*Q;

C[2]=-0.625 + (-0.25 + K/2.)*K;

C[3]=(-0.75 + (0.16666666666666666 - K/3.)*K)*Q;

C[4]=0.65625 + K*(-0.020833333333333332 + (-0.125 + K/4.)*K);

C[5]=(1.675 + K*(0.016666666666666666 + (0.1 - K/5.)*K))*Q;

C[6]=-1.09375 + K*(1.1041666666666667 + K*(-0.013888888888888888 + (-0.08333333333333333 + K/6.)*K));

C[7]=(-4.258928571428571 + K*(0.005952380952380952 + K*(0.011904761904761904 + (0.07142857142857142 - K/7.)*K)))*Q;

C[8]=2.12265625 + K*(-5.600520833333333 + K*(-0.005208333333333333 + K*(-0.010416666666666666 + (-0.0625 + K/8.)*K)));

C[9]=(11.015972222222222 + K*(-2.484722222222222 + K*(0.004629629629629629 + K*(0.009259259259259259 + (0.05555555555555555 - K/9.)*K))))*Q;

C[10]=-4.1965625 + K*(21.643125 + K*(-0.002638888888888889 + K*(-0.004166666666666667 + K*(-0.008333333333333333 + (-0.05 + K/10.)*K))));

C[11]=(-26.844602272727272 + K*(19.068371212121214 + K*(0.002398989898989899 + K*(0.003787878787878788 + K*(0.007575757575757576 + (0.045454545454545456 - K/11.)*K)))))*Q;

C[12]=7.555710565476191 + K*(-69.34879712301587 + K*(6.353993055555556 + K*(-0.002199074074074074 + K*(-0.003472222222222222 + K*(-0.006944444444444444 + (-0.041666666666666664 + K/12.)*K)))));

C[13]=(56.00306204212454 + K*(-90.51649496336996 + K*(0.0014423076923076924 + K*(0.00202991452991453 + K*(0.003205128205128205 + K*(0.00641025641025641 + (0.038461538461538464 - K/13.)*K))))))*Q;

C[14]=-10.137523915816326 + K*(174.73393388605442 + K*(-59.71027848639456 + K*(-0.0013392857142857143 + K*(-0.001884920634920635 + K*(-0.002976190476190476 + K*(-0.005952380952380952 + (-0.03571428571428571 + K/14.)*K))))));

C[15]=(-79.07677827380952 + K*(294.70178075396825 + K*(-15.921517857142858 + K*(0.00125 + K*(0.0017592592592592592 + K*(0.002777777777777778 + K*(0.005555555555555556 + (0.03333333333333333 - K/15.)*K)))))))*Q;

C[16]=1.8184256417410714 + K*(-263.96002371651787 + K*(284.15770554315475 + K*(-0.0008918237433862434 + K*(-0.001171875 + K*(-0.0016493055555555556 + K*(-0.0026041666666666665 + K*(-0.005208333333333333 + (-0.03125 + K/16.)*K)))))));

C[17]=(-23.194026829481793 + K*(-492.6884825805322 + K*(148.782943802521 + K*(0.0008393635231870526 + K*(0.0011029411764705882 + K*(0.0015522875816993463 + K*(0.0024509803921568627 + K*(0.004901960784313725 + (0.029411764705882353 - K/17.)*K))))))))*Q;

C[18]=40.22334852430556 + K*(-277.2962258184524 + K*(-562.4775210813492 + K*(33.06209628527337 + K*(-0.0007927322163433275 + K*(-0.0010416666666666667 + K*(-0.0014660493827160495 + K*(-0.0023148148148148147 + K*(-0.004629629629629629 + (-0.027777777777777776 + K/18.)*K))))))));

C[19]=(546.8550096921992 + K*(-1114.8397936899541 + K*(-399.53829665309104 + K*(0.0005982839042049568 + K*(0.0007510094681147313 + K*(0.000986842105263158 + K*(0.001388888888888889 + K*(0.0021929824561403508 + K*(0.0043859649122807015 + (0.02631578947368421 - K/19.)*K)))))))))*Q;

C[20]=-106.91457501775568 + K*(3186.0308820938176 + K*(-2361.2530055183533 + K*(-166.40644225363758 + K*(-0.000568369708994709 + K*(-0.0007134589947089947 + K*(-0.0009375 + K*(-0.0013194444444444445 + K*(-0.0020833333333333333 + K*(-0.004166666666666667 + (-0.025 + K/20.)*K)))))))));

C[21]=(-1294.3548559212984 + K*(10574.18993230294 + K*(-2925.227625129913 + K*(-31.695930531934998 + K*(0.0005413044847568657 + K*(0.0006794847568657093 + K*(0.0008928571428571428 + K*(0.0012566137566137566 + K*(0.001984126984126984 + K*(0.003968253968253968 + (0.023809523809523808 - K/21.)*K))))))))))*Q;

C[22]=-91.34462044155536 + K*(-6881.736009172231 + K*(22198.722893579157 + K*(-2133.1054577583873 + K*(-0.0004252971180054513 + K*(-0.0005166997354497354 + K*(-0.0006485990860990861 + K*(-0.0008522727272727272 + K*(-0.0011994949494949494 + K*(-0.001893939393939394 + K*(-0.003787878787878788 + (-0.022727272727272728 + K/22.)*K))))))))));

C[23]=(-2557.4219362056365 + K*(-21249.469819307447 + K*(30705.266603346645 + K*(-847.9086074627617 + K*(0.00040680593896173605 + K*(0.0004942345295606165 + K*(0.0006203991258339084 + K*(0.0008152173913043478 + K*(0.001147342995169082 + K*(0.0018115942028985507 + K*(0.0036231884057971015 + (0.021739130434782608 - K/23.)*K)))))))))))*Q;

C[24]=1525.499359748528 + K*(-24831.522604565165 + K*(-42440.990800023814 + K*(28049.602818618194 + K*(-141.31848729263118 + K*(-0.0003898556915049971 + K*(-0.00047364142416225747 + K*(-0.0005945491622574956 + K*(-0.00078125 + K*(-0.001099537037037037 + K*(-0.001736111111111111 + K*(-0.003472222222222222 + (-0.020833333333333332 + K/24.)*K)))))))))));

C[25]=(27124.075061837706 + K*(-128458.77184957685 + K*(-57773.22507086603 + K*(16332.256116348755 + K*(0.00031570216049382717 + K*(0.0003742614638447972 + K*(0.00045469576719576717 + K*(0.0005707671957671958 + K*(0.00075 + K*(0.0010555555555555555 + K*(0.0016666666666666668 + K*(0.0033333333333333335 + (0.02 - K/25.)*K))))))))))))*Q;

C[26]=-3479.831401071407 + K*(215453.99821883257 + K*(-413436.90007582813 + K*(-54942.60059336244 + K*(5498.61020490818 + K*(-0.00030355976970560303 + K*(-0.0003598667921584588 + K*(-0.00043720746845746846 + K*(-0.0005488146113146114 + K*(-0.0007211538461538462 + K*(-0.001014957264957265 + K*(-0.0016025641025641025 + K*(-0.003205128205128205 + (-0.019230769230769232 + K/26.)*K))))))))))));

C[27]=(-49965.76250289681 + K*(1.0180869185420631e6 + K*(-888957.4315148331 + K*(-36607.78511840427 + K*(814.6092092392454 + K*(0.0002923168152720622 + K*(0.0003465383924488863 + K*(0.00042101459925534 + K*(0.0005284881442288849 + K*(0.0006944444444444445 + K*(0.000977366255144033 + K*(0.0015432098765432098 + K*(0.0030864197530864196 + (0.018518518518518517 - K/27.)*K)))))))))))))*Q;

C[28]=-13199.704855963786 + K*(-304114.4479332554 + K*(3.2031234528838634e6 + K*(-1.3186978751671617e6 + K*(-16618.87985133844 + K*(-0.00024235178516552523 + K*(-0.0002818769290123457 + K*(-0.0003341620212899975 + K*(-0.0004059783635676493 + K*(-0.000509613567649282 + K*(-0.0006696428571428571 + K*(-0.0009424603174603175 + K*(-0.001488095238095238 + K*(-0.002976190476190476 + (-0.017857142857142856 + K/28.)*K)))))))))))));

C[29]=(-339564.09571017075 + K*(-981517.7637782916 + K*(7.093994639768049e6 + K*(-1.3591003537274913e6 + K*(-4691.883327869058 + K*(0.0002339948270563692 + K*(0.0002721570349084717 + K*(0.00032263919296965273 + K*(0.00039197910965152347 + K*(0.0004920406860062032 + K*(0.000646551724137931 + K*(0.0009099616858237548 + K*(0.0014367816091954023 + K*(0.0028735632183908046 + (0.017241379310344827 - K/29.)*K))))))))))))))*Q;

C[30]=103096.29341112258 + K*(-3.741784859996233e6 + K*(-1.5421956291996404e6 + K*(1.1368730435012683e7 + K*(-957939.1735305398 + K*(-625.5846684214624 + K*(-0.00022619499948782357 + K*(-0.000263085133744856 + K*(-0.00031188455320399765 + K*(-0.000378913139329806 + K*(-0.00047563932980599645 + K*(-0.000625 + K*(-0.0008796296296296296 + K*(-0.001388888888888889 + K*(-0.002777777777777778 + (-0.016666666666666666 + K/30.)*K))))))))))))));

C[31]=(2.1833472795800082e6 + K*(-2.4094951583361197e7 + K*(376055.4847053262 + K*(1.3305895284872284e7 + K*(-441038.92459867854 + K*(0.0001910985939463762 + K*(0.00021889838660111958 + K*(0.00025459851652727996 + K*(0.000301823761165159 + K*(0.0003666901348352961 + K*(0.00046029612561870626 + K*(0.0006048387096774194 + K*(0.0008512544802867384 + K*(0.0013440860215053765 + K*(0.002688172043010753 + (0.016129032258064516 - K/31.)*K)))))))))))))))*Q;

C[32]=-34009.85985759633 + K*(2.1088024974256773e7 + K*(-1.0283676144559164e8 + K*(7.494989145302481e6 + K*(1.1299051475575613e7 + K*(-119614.84626551632 + K*(-0.00018512676288555196 + K*(-0.0002120578120198346 + K*(-0.0002466423128858025 + K*(-0.0002923917686287478 + K*(-0.00035523106812169314 + K*(-0.0004459118716931217 + K*(-0.0005859375 + K*(-0.0008246527777777778 + K*(-0.0013020833333333333 + K*(-0.0026041666666666665 + (-0.015625 + K/32.)*K)))))))))))))));

C[33]=(1.187932182006185e6 + K*(1.2378668963125809e8 + K*(-3.104822545625931e8 + K*(1.8201616029603697e7 + K*(6.792273162088149e6 + K*(-14498.769065781376 + K*(0.00017951686097992915 + K*(0.00020563181771620325 + K*(0.00023916830340441452 + K*(0.00028353141200363423 + K*(0.0003444664902998236 + K*(0.00043239939073272404 + K*(0.0005681818181818182 + K*(0.0007996632996632996 + K*(0.0012626262626262627 + K*(0.0025252525252525255 + (0.015151515151515152 - K/33.)*K))))))))))))))))*Q;

C[34]=-2.3759161383546586e6 + K*(3.3102742665377446e7 + K*(4.957690946986563e8 + K*(-6.877213210538577e8 + K*(2.5254240618506655e7 + K*(2.7437802316445024e6 + K*(-0.00015402038993971427 + K*(-0.0001742369533040489 + K*(-0.00019958382307749137 + K*(-0.0002321339415395788 + K*(-0.00027519225282705677 + K*(-0.00033433512293806414 + K*(-0.0004196817615935263 + K*(-0.0005514705882352941 + K*(-0.0007761437908496732 + K*(-0.0012254901960784314 + K*(-0.0024509803921568627 + (-0.014705882352941176 + K/34.)*K))))))))))))))));

C[35]=(-6.441195072764427e7 + K*(3.473587249424732e8 + K*(1.4399574625710392e9 + K*(-1.139610442446717e9 + K*(2.29370639989353e7 + K*(668577.3781775468 + K*(0.00014961980737000815 + K*(0.00016925875463821892 + K*(0.0001938814281324202 + K*(0.00022550154320987654 + K*(0.000267329617031998 + K*(0.00032478269085411943 + K*(0.00040769085411942557 + K*(0.0005357142857142857 + K*(0.000753968253968254 + K*(0.0011904761904761906 + K*(0.002380952380952381 + (0.014285714285714285 - K/35.)*K)))))))))))))))))*Q;

C[36]=8.113072831988651e6 + K*(-7.95275504545533e8 + K*(2.1418801947834523e9 + K*(3.1434138336441584e9 + K*(-1.4233734119278417e9 + K*(1.3916615498279778e7 + K*(74286.37520828104 + K*(-0.00014546370160973014 + K*(-0.00016455712256493505 + K*(-0.00018849583290651964 + K*(-0.00021923761145404663 + K*(-0.0002599037943366647 + K*(-0.000315760949441505 + K*(-0.00039636610817166373 + K*(-0.0005208333333333333 + K*(-0.0007330246913580247 + K*(-0.0011574074074074073 + K*(-0.0023148148148148147 + (-0.013888888888888888 + K/36.)*K)))))))))))))))));

C[37]=(1.7186725830685458e8 + K*(-5.984889036559886e9 + K*(8.915215352457127e9 + K*(5.267664704664617e9 + K*(-1.3359468715042915e9 + K*(5.460120063194431e6 + K*(0.00012641887586600716 + K*(0.00014153225021487257 + K*(0.00016010963276588276 + K*(0.00018340135093607317 + K*(0.00021331227060393727 + K*(0.0002528793674627008 + K*(0.00030722686972686975 + K*(0.00038565351065351065 + K*(0.0005067567567567568 + K*(0.0007132132132132132 + K*(0.0011261261261261261 + K*(0.0022522522522522522 + (0.013513513513513514 - K/37.)*K))))))))))))))))))*Q;

C[38]=4.845358754700961e7 + K*(1.5807191179176028e9 + K*(-3.091045161637381e10 + K*(2.676332064610932e10 + K*(6.851422485817298e9 + K*(-9.287763795488605e8 + K*(1.256152900141858e6 + K*(-0.0001230920633432175 + K*(-0.0001378077173144812 + K*(-0.0001558962213773069 + K*(-0.00017857499959565018 + K*(-0.00020769878979857051 + K*(-0.0002462246472663139 + K*(-0.0002991419521024784 + K*(-0.00037550473405736565 + K*(-0.000493421052631579 + K*(-0.0006944444444444445 + K*(-0.0010964912280701754 + K*(-0.0021929824561403508 + (-0.013157894736842105 + K/38.)*K))))))))))))))))));

C[39]=(1.688862409525175e9 + K*(7.943841970381187e9 + K*(-1.1672038467034108e11 + K*(6.008760751553745e10 + K*(6.933916635401379e9 + K*(-4.6425055682111317e8 + K*(128836.19500579652 + K*(0.00011993585659082729 + K*(0.00013427418610128936 + K*(0.00015189888236763236 + K*(0.00017399615345217197 + K*(0.00020237317980373537 + K*(0.00023991119477230588 + K*(0.0002914716456383123 + K*(0.0003658764075430742 + K*(0.0004807692307692308 + K*(0.0006766381766381767 + K*(0.0010683760683760685 + K*(0.002136752136752137 + (0.01282051282051282 - K/39.)*K)))))))))))))))))))*Q;

C[40]=-4.256211096941436e8 + K*(2.6144641684354103e10 + K*(2.0347873846253147e10 + K*(-3.346459087991558e11 + K*(1.0294384887182762e11 + K*(5.426898698551563e9 + K*(-1.5783949079684484e8 + K*(-0.00010537380597513682 + K*(-0.00011693746017605661 + K*(-0.00013091733144875712 + K*(-0.00014810141030844156 + K*(-0.00016964624961586768 + K*(-0.00019731385030864198 + K*(-0.00023391341490299822 + K*(-0.0002841848544973545 + K*(-0.00035672949735449734 + K*(-0.00046875 + K*(-0.0006597222222222222 + K*(-0.0010416666666666667 + K*(-0.0020833333333333333 + (-0.0125 + K/40.)*K)))))))))))))))))));

/*

Mathematica generator of Aunemco.txt

T[z_] = z + z^3 + q z^4
P[m_, L_] := Sum[a[m, n] L^n, {n, 0, IntegerPart[m/2]}]
A[1, 0] = -q; A[1, 1] = 0;
a[2, 0] = 0; A[2, 0] = 0;
m = 2; s[m] = Numerator[ Normal[Series[(T[F[m, -1/x^2]] - F[m, -1/x^2 + 1]) 2^((m + 1)/2)/x^(m + 2), {x, 0, 1}]]]
t[m] = Numerator[Coefficient[Normal[s[m]], x] ]
sub[m] = Extract[Solve[t[m] == 0, a[m, 1]], 1]
F[m_, z_] := 1/(-2 z)^(1/2) (1 - q/(-2 z)^(1/2) + Sum[P[n, Log[-z]]/(-2 z)^(n/2), {n, 2, m}])
f[m, z_] = ReplaceAll[F[m, z], SUB[m]]

m = 3
s[m] = Simplify[
   ReplaceAll[
    Series[(T[F[m, -1/x^2]] - F[m, -1/x^2 + 1]) 2^((m + 3)/2)/
       x^(m + 3), {x, 0, 0}], SUB[m - 1]]];
t[m] = ReplaceAll[Normal[s[m]], Log[x] -> L];
u[m] = Table[
   Coefficient[t[m] L, L^n] == 0, {n, 1, 1 + IntegerPart[m/2]}];
tab[m] = Table[a[m, n], {n, 0, IntegerPart[m/2]}];
sub[m] = Extract[Solve[u[m], tab[m]], 1]
SUB[m] = Join[SUB[m - 1], sub[m]];

f[m, z_] = ReplaceAll[F[m, z], SUB[m]]

Series[Simplify[f[m, -1/2/x^2], x > 0], {x, 0, 3}]

m = 4; s[m] =
 Simplify[ReplaceAll[
   Series[(T[F[m, -1/x^2]] - F[m, -1/x^2 + 1]) 2^((m + 3)/2)/
      x^(m + 3), {x, 0, 0}], SUB[m - 1]]];
t[m] = ReplaceAll[Normal[s[m]], Log[x] -> L];
u[m] = Table[
   Coefficient[t[m] L, L^n] == 0, {n, 1, 1 + IntegerPart[m/2]}];
tab[m] = Table[a[m, n], {n, 0, IntegerPart[m/2]}];
sub[m] = Extract[Solve[u[m], tab[m]], 1]
SUB[m] = Join[SUB[m - 1], sub[m]];
f[m, z_] = ReplaceAll[F[m, z], SUB[m]];

fs[x_] = Simplify[f[m, -1/2/x^2], x > 0]

gs[x_] = x + q x^2 + b x^3 Log[x]; gs1 = Series[fs[gs[x]] - x, {x, 0, 3}]

gs2 = Coefficient[Normal[gs1], x^3]

sg1 = Series[g2[f[4, -1/x^2]] + 1/x^2, {x, 0, 1}]

g3[x_] = -1/(2 x^2) + q/x + q^2/2 + 1/4 (3 + 2 q^2) Log[2] + 1/2 (3 + 2 q^2) Log[x] + q (1/2 - q^2) x + c2 x^2;

sg3 = Simplify[Sqrt[2] Series[g3[f[4, -1/x^2]] + 1/x^2, {x, 0, 2}]]

G[m_, x_] := -1/(2 x^2) + q/x + q^2/2 + 1/4 (3 + 2 q^2) Log[2] + 1/2 (3 + 2 q^2) Log[x] + Sum[c[n] x^n, {n, 1, m}]

m = 1; sg[m] = Coefficient[Series[G[m + 3, T[z]] - G[m + 3, z] - 1, {z, 0, 3}], z^(m + 2)]

st[m] = Solve[sg[m] == 0, c[m]]

su[m] = Extract[st[m], 1]

SU[m] = su[m]

m = 2; sf[m] = Series[ ReplaceAll[G[m + 3, T[z]] - G[m + 3, z] - 1, SU[m - 1]], {z, 0, m + 2}]

sg[m] = Simplify[Coefficient[sf[m] 2^m, z^4]]

st[m] = Solve[sg[m] == 0, c[m]]

su[m] = Extract[st[m], 1]

SU[m] = Join[SU[m - 1], su[m]]

m = 3;
sf[m] = Series[ ReplaceAll[G[m + 3, T[z]] - G[m + 3, z] - 1, SU[m - 1]], {z, 0, m + 2}]
sg[m] = Simplify[Coefficient[sf[m] 2^m, z^(m + 2)]]
st[m] = Solve[sg[m] == 0, c[m]]
su[m] = Extract[st[m], 1]
SU[m] = Join[SU[m - 1], su[m]]

m = 4;
sf[m] = Series[ ReplaceAll[G[m + 3, T[z]] - G[m + 3, z] - 1, SU[m - 1]], {z, 0, m + 2}];
sg[m] = Simplify[Coefficient[sf[m] 2^m, z^(m + 2)]];
st[m] = Solve[sg[m] == 0, c[m]];
su[m] = Extract[st[m], 1];
SU[m] = Join[SU[m - 1], su[m]]

..

For[m=1, m<41, Print["C[", m, "]=", CForm[ReplaceAll[HornerForm[ReplaceAll[c[m],SU[m]]], {q^2 -> K, q -> Q}]], ";"]; m++;]

Keywords

Abel function ArqNem AuNem Book C++ Mathematica Nemtsov function Superfunctions */