zeta.c

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY without ev

  1.00000000000000000000000000040,
  1.00000000000000000000000000020,
  1.00000000000000000000000000010,
  1.00000000000000000000000000005,
  1.00000000000000000000000000003,
  1.00000000000000000000000000001,
  1.00000000000000000000000000001,
  1.00000000000000000000000000000,
  1.00000000000000000000000000000,
  1.00000000000000000000000000000
};
#endif /* 0 */


/* zeta(n) - 1 */
#define ZETA_POS_TABLE_NMAX   100
static double zetam1_pos_int_table[ZETA_POS_TABLE_NMAX+1] = {
 -1.5,                               /* zeta(0) */
  0.0,       /* FIXME: Infinity */   /* zeta(1) - 1 */
  0.644934066848226436472415166646,  /* zeta(2) - 1 */
  0.202056903159594285399738161511,
  0.082323233711138191516003696541,
  0.036927755143369926331365486457,
  0.017343061984449139714517929790,
  0.008349277381922826839797549849,
  0.004077356197944339378685238508,
  0.002008392826082214417852769232,
  0.000994575127818085337145958900,
  0.000494188604119464558702282526,
  0.000246086553308048298637998047,
  0.000122713347578489146751836526,
  0.000061248135058704829258545105,
  0.000030588236307020493551728510,
  0.000015282259408651871732571487,
  7.6371976378997622736002935630e-6,
  3.8172932649998398564616446219e-6,
  1.9082127165539389256569577951e-6,
  9.5396203387279611315203868344e-7,
  4.7693298678780646311671960437e-7,
  2.3845050272773299000364818675e-7,
  1.1921992596531107306778871888e-7,
  5.9608189051259479612440207935e-8,
  2.9803503514652280186063705069e-8,
  1.4901554828365041234658506630e-8,
  7.4507117898354294919810041706e-9,
  3.7253340247884570548192040184e-9,
  1.8626597235130490064039099454e-9,
  9.3132743241966818287176473502e-10,
  4.6566290650337840729892332512e-10,
  2.3283118336765054920014559759e-10,
  1.1641550172700519775929738354e-10,
  5.8207720879027008892436859891e-11,
  2.9103850444970996869294252278e-11,
  1.4551921891041984235929632245e-11,
  7.2759598350574810145208690123e-12,
  3.6379795473786511902372363558e-12,
  1.8189896503070659475848321007e-12,
  9.0949478402638892825331183869e-13,
  4.5474737830421540267991120294e-13,
  2.2737368458246525152268215779e-13,
  1.1368684076802278493491048380e-13,
  5.6843419876275856092771829675e-14,
  2.8421709768893018554550737049e-14,
  1.4210854828031606769834307141e-14,
  7.1054273952108527128773544799e-15,
  3.5527136913371136732984695340e-15,
  1.7763568435791203274733490144e-15,
  8.8817842109308159030960913863e-16,
  4.4408921031438133641977709402e-16,
  2.2204460507980419839993200942e-16,
  1.1102230251410661337205445699e-16,
  5.5511151248454812437237365905e-17,
  2.7755575621361241725816324538e-17,
  1.3877787809725232762839094906e-17,
  6.9388939045441536974460853262e-18,
  3.4694469521659226247442714961e-18,
  1.7347234760475765720489729699e-18,
  8.6736173801199337283420550673e-19,
  4.3368086900206504874970235659e-19,
  2.1684043449972197850139101683e-19,
  1.0842021724942414063012711165e-19,
  5.4210108624566454109187004043e-20,
  2.7105054312234688319546213119e-20,
  1.3552527156101164581485233996e-20,
  6.7762635780451890979952987415e-21,
  3.3881317890207968180857031004e-21,
  1.6940658945097991654064927471e-21,
  8.4703294725469983482469926091e-22,
  4.2351647362728333478622704833e-22,
  2.1175823681361947318442094398e-22,
  1.0587911840680233852265001539e-22,
  5.2939559203398703238139123029e-23,
  2.6469779601698529611341166842e-23,
  1.3234889800848990803094510250e-23,
  6.6174449004244040673552453323e-24,
  3.3087224502121715889469563843e-24,
  1.6543612251060756462299236771e-24,
  8.2718061255303444036711056167e-25,
  4.1359030627651609260093824555e-25,
  2.0679515313825767043959679193e-25,
  1.0339757656912870993284095591e-25,
  5.1698788284564313204101332166e-26,
  2.5849394142282142681277617708e-26,
  1.2924697071141066700381126118e-26,
  6.4623485355705318034380021611e-27,
  3.2311742677852653861348141180e-27,
  1.6155871338926325212060114057e-27,
  8.0779356694631620331587381863e-28,
  4.0389678347315808256222628129e-28,
  2.0194839173657903491587626465e-28,
  1.0097419586828951533619250700e-28,
  5.0487097934144756960847711725e-29,
  2.5243548967072378244674341938e-29,
  1.2621774483536189043753999660e-29,
  6.3108872417680944956826093943e-30,
  3.1554436208840472391098412184e-30,
  1.5777218104420236166444327830e-30,
  7.8886090522101180735205378276e-31
};


#define ZETA_NEG_TABLE_NMAX  99
#define ZETA_NEG_TABLE_SIZE  50
static double zeta_neg_int_table[ZETA_NEG_TABLE_SIZE] = {
 -0.083333333333333333333333333333,     /* zeta(-1) */
  0.008333333333333333333333333333,     /* zeta(-3) */
 -0.003968253968253968253968253968,     /* ...      */
  0.004166666666666666666666666667,
 -0.007575757575757575757575757576,
  0.021092796092796092796092796093,
 -0.083333333333333333333333333333,
  0.44325980392156862745098039216,
 -3.05395433027011974380395433027,
  26.4562121212121212121212121212,
 -281.460144927536231884057971014,
  3607.5105463980463980463980464,
 -54827.583333333333333333333333,
  974936.82385057471264367816092,
 -2.0052695796688078946143462272e+07,
  4.7238486772162990196078431373e+08,
 -1.2635724795916666666666666667e+10,
  3.8087931125245368811553022079e+11,
 -1.2850850499305083333333333333e+13,
  4.8241448354850170371581670362e+14,
 -2.0040310656516252738108421663e+16,
  9.1677436031953307756992753623e+17,
 -4.5979888343656503490437943262e+19,
  2.5180471921451095697089023320e+21,
 -1.5001733492153928733711440151e+23,
  9.6899578874635940656497942895e+24,
 -6.7645882379292820990945242302e+26,
  5.0890659468662289689766332916e+28,
 -4.1147288792557978697665486068e+30,
  3.5666582095375556109684574609e+32,
 -3.3066089876577576725680214670e+34,
  3.2715634236478716264211227016e+36,
 -3.4473782558278053878256455080e+38,
  3.8614279832705258893092720200e+40,
 -4.5892974432454332168863989006e+42,
  5.7775386342770431824884825688e+44,
 -7.6919858759507135167410075972e+46,
  1.0813635449971654696354033351e+49,
 -1.6029364522008965406067102346e+51,
  2.5019479041560462843656661499e+53,
 -4.1067052335810212479752045004e+55,
  7.0798774408494580617452972433e+57,
 -1.2804546887939508790190849756e+60,
  2.4267340392333524078020892067e+62,
 -4.8143218874045769355129570066e+64,
  9.9875574175727530680652777408e+66,
 -2.1645634868435185631335136160e+69,
  4.8962327039620553206849224516e+71,    /* ...        */
 -1.1549023923963519663954271692e+74,    /* zeta(-97)  */
  2.8382249570693706959264156336e+76     /* zeta(-99)  */
};


/* coefficients for Maclaurin summation in hzeta()
 * B_{2j}/(2j)!
 */
static double hzeta_c[15] = {
  1.00000000000000000000000000000,
  0.083333333333333333333333333333,
 -0.00138888888888888888888888888889,
  0.000033068783068783068783068783069,
 -8.2671957671957671957671957672e-07,
  2.0876756987868098979210090321e-08,
 -5.2841901386874931848476822022e-10,
  1.3382536530684678832826980975e-11,
 -3.3896802963225828668301953912e-13,
  8.5860620562778445641359054504e-15,
 -2.1748686985580618730415164239e-16,
  5.5090028283602295152026526089e-18,
 -1.3954464685812523340707686264e-19,
  3.5347070396294674716932299778e-21,
 -8.9535174270375468504026113181e-23
};

#define ETA_POS_TABLE_NMAX  100
static double eta_pos_int_table[ETA_POS_TABLE_NMAX+1] = {
0.50000000000000000000000000000,  /* eta(0) */
M_LN2,                            /* eta(1) */
0.82246703342411321823620758332,  /* ...    */
0.90154267736969571404980362113,
0.94703282949724591757650323447,
0.97211977044690930593565514355,
0.98555109129743510409843924448,
0.99259381992283028267042571313,
0.99623300185264789922728926008,
0.99809429754160533076778303185,
0.99903950759827156563922184570,
0.99951714349806075414409417483,
0.99975768514385819085317967871,
0.99987854276326511549217499282,
0.99993917034597971817095419226,
0.99996955121309923808263293263,
0.99998476421490610644168277496,
0.99999237829204101197693787224,
0.99999618786961011347968922641,
0.99999809350817167510685649297,
0.99999904661158152211505084256,
0.99999952325821554281631666433,
0.99999976161323082254789720494,
0.99999988080131843950322382485,
0.99999994039889239462836140314,
0.99999997019885696283441513311,
0.99999998509923199656878766181,
0.99999999254955048496351585274,
0.99999999627475340010872752767,
0.99999999813736941811218674656,
0.99999999906868228145397862728,
0.99999999953434033145421751469,
0.99999999976716989595149082282,
0.99999999988358485804603047265,
0.99999999994179239904531592388,
0.99999999997089618952980952258,
0.99999999998544809143388476396,
0.99999999999272404460658475006,
0.99999999999636202193316875550,
0.99999999999818101084320873555,
0.99999999999909050538047887809,
0.99999999999954525267653087357,
0.99999999999977262633369589773,
0.99999999999988631316532476488,
0.99999999999994315658215465336,
0.99999999999997157829090808339,
0.99999999999998578914539762720,
0.99999999999999289457268000875,
0.99999999999999644728633373609,
0.99999999999999822364316477861,
0.99999999999999911182158169283,
0.99999999999999955591079061426,
0.99999999999999977795539522974,
0.99999999999999988897769758908,
0.99999999999999994448884878594,
0.99999999999999997224442439010,
0.99999999999999998612221219410,
0.99999999999999999306110609673,
0.99999999999999999653055304826,
0.99999999999999999826527652409,
0.99999999999999999913263826204,
0.99999999999999999956631913101,
0.99999999999999999978315956551,
0.99999999999999999989157978275,
0.99999999999999999994578989138,
0.99999999999999999997289494569,
0.99999999999999999998644747284,
0.99999999999999999999322373642,
0.99999999999999999999661186821,
0.99999999999999999999830593411,
0.99999999999999999999915296705,
0.99999999999999999999957648353,
0.99999999999999999999978824176,
0.99999999999999999999989412088,
0.99999999999999999999994706044,
0.99999999999999999999997353022,
0.99999999999999999999998676511,
0.99999999999999999999999338256,
0.99999999999999999999999669128,
0.99999999999999999999999834564,
0.99999999999999999999999917282,
0.99999999999999999999999958641,
0.99999999999999999999999979320,
0.99999999999999999999999989660,
0.99999999999999999999999994830,
0.99999999999999999999999997415,
0.99999999999999999999999998708,
0.99999999999999999999999999354,
0.99999999999999999999999999677,
0.99999999999999999999999999838,
0.99999999999999999999999999919,
0.99999999999999999999999999960,
0.99999999999999999999999999980,
0.99999999999999999999999999990,
0.99999999999999999999999999995,
0.99999999999999999999999999997,
0.99999999999999999999999999999,
0.99999999999999999999999999999,
1.00000000000000000000000000000,
1.00000000000000000000000000000,
1.00000000000000000000000000000,
};


#define ETA_NEG_TABLE_NMAX  99
#define ETA_NEG_TABLE_SIZE  50
static double eta_neg_int_table[ETA_NEG_TABLE_SIZE] = {
 0.25000000000000000000000000000,   /* eta(-1) */
-0.12500000000000000000000000000,   /* eta(-3) */
 0.25000000000000000000000000000,   /* ...      */
-1.06250000000000000000000000000,
 7.75000000000000000000000000000,
-86.3750000000000000000000000000,
 1365.25000000000000000000000000,
-29049.0312500000000000000000000,
 800572.750000000000000000000000,
-2.7741322625000000000000000000e+7,
 1.1805291302500000000000000000e+9,
-6.0523980051687500000000000000e+10,
 3.6794167785377500000000000000e+12,
-2.6170760990658387500000000000e+14,
 2.1531418140800295250000000000e+16,
-2.0288775575173015930156250000e+18,
 2.1708009902623770590275000000e+20,
-2.6173826968455814932120125000e+22,
 3.5324148876863877826668602500e+24,
-5.3042033406864906641493838981e+26,
 8.8138218364311576767253114668e+28,
-1.6128065107490778547354654864e+31,
 3.2355470001722734208527794569e+33,
-7.0876727476537493198506645215e+35,
 1.6890450341293965779175629389e+38,
-4.3639690731216831157655651358e+40,
 1.2185998827061261322605065672e+43,
-3.6670584803153006180101262324e+45,
 1.1859898526302099104271449748e+48,
-4.1120769493584015047981746438e+50,
 1.5249042436787620309090168687e+53,
-6.0349693196941307074572991901e+55,
 2.5437161764210695823197691519e+58,
-1.1396923802632287851130360170e+61,
 5.4180861064753979196802726455e+63,
-2.7283654799994373847287197104e+66,
 1.4529750514918543238511171663e+69,
-8.1705519371067450079777183386e+71,
 4.8445781606678367790247757259e+74,
-3.0246694206649519336179448018e+77,
 1.9858807961690493054169047970e+80,
-1.3694474620720086994386818232e+83,
 9.9070382984295807826303785989e+85,