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// y-cruncher Custom Formula File
//
// This can be loaded directly from the Custom Compute menu or
// entered from the command line as "custom:filename.cfg".
// y-cruncher custom custom:"filename.cfg"
//
//
// Author: Alexander J. Yee
// Date: October 4, 2018
//
// Value = 1.03692775514336992633136548645703416805708091950191...
//
// Original Formula: Broadhurst (1998)
// https://arxiv.org/pdf/math/9803067.pdf
//
// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 )
// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------)
// 62651 k=0 16^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
//
// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 )
// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------)
// 250604 k=0 4096^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
//
// 369 inf 1 ( 131072 4096 1024 128 4 1 )
// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------)
// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 )
//
//
// Optimized into a massive 74-term BBP formula by Alex Yee (2018).
// The following implementation groups the 74 terms into sets of 2 or 3 terms each.
//
{
NameShort : "Zeta(5)"
NameLong : "Zeta(5)"
AlgorithmShort : "Broadhurst (optimized)"
AlgorithmLong : "Broadhurst (1998) (optimized)"
Formula : {
LinearCombination : [
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1762059375
Alternating : "false"
PowerCoef : -30
PowerShift : 12
PolynomialP : [
55293739267 -2260658245680 40544723556900 -418475704423680
2743554653514720 -11903795644396032 34544269695818880 -66159912056279040
80125279389331200 -55550303705640960 16795225145889792
]
PolynomialQ : [
-3125 143750 -2982500 36979000
-306192400 1793303776 -7678751040 24504739200
-58849079040 106537628160 -144464145408 144349931520
-103061237760 49716633600 -14511882240 1934917632
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 117470625
Alternating : "true"
PowerCoef : -30
PowerShift : 18
PolynomialP : [
-34509025 693618140 -5558112160 22244671360 -44497491200 35600165888
]
PolynomialQ : [
243 -6480 75600 -506880
2158080 -6086656 11509760 -14417920
11468800 -5242880 1048576
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 563859
Alternating : "false"
PowerCoef : -30
PowerShift : 30
PolynomialP : [
-1192566547 8419823750 -23837731000 33810670000 -24015350000 6831500000
]
PolynomialQ : [
992436543 -12602368800 71888512500 -242585280000
536262300000 -811465600000 851210000000 -611200000000
287500000000 -80000000000 10000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 563859
Alternating : "false"
PowerCoef : -30
PowerShift : 12
PolynomialP : [
-322657 7619750 -95641000 767230000 -3520850000 6831500000
]
PolynomialQ : [
243 -16200 472500 -7920000
84300000 -594400000 2810000000 -8800000000
17500000000 -20000000000 10000000000
]
}}]
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CoefficientP : 1
CoefficientQ : 0
CoefficientD : 195784375
Alternating : "true"
PowerCoef : -30
PowerShift : 27
PolynomialP : [
-19669507184511 169174898363340 -581291762951520 997878572323200
-856076349070080 293675932965888
]
PolynomialQ : [
2706784157 -37965284280 238310226000 -881506644480
2127741073920 -3501690310656 3979152138240 -3082968760320
1558683648000 -464380231680 61917364224
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 195784375
Alternating : "true"
PowerCoef : -30
PowerShift : 12
PolynomialP : [
2423887983 27619171020 -1493511864480 19915706597760
-121886516655360 293675932965888
]
PolynomialQ : [
3125 -225000 6930000 -119232000
1257638400 -8429432832 36219985920 -98895790080
165542952960 -154793410560 61917364224
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "true"
PowerCoef : -30
PowerShift : 35
PolynomialP : [
-289888774695 1755263684500 -4235370300000 5093670800000
-3054636000000 731024000000
]
PolynomialQ : [
3515706497843 -39184344867600 196460896610000 -583507923840000
1136939844800000 -1518525619200000 1407975040000000 -894873600000000
373120000000000 -92160000000000 10240000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "true"
PowerCoef : -30
PowerShift : 26
PolynomialP : [
-54164342135 475456051500 -1676786300000 2968479600000
-2636908000000 939888000000
]
PolynomialQ : [
59797108943 -1003587842400 7573696130000 -33843912960000
99171300800000 -199112140800000 277402240000000 -264806400000000
165760000000000 -61440000000000 10240000000000
]
}}]
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CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "true"
PowerCoef : -30
PowerShift : 20
PolynomialP : [
-6315035675 84097131500 -453365420000 1234908400000
-1697020000000 939888000000
]
PolynomialQ : [
992436543 -25204737600 287554050000 -1940682240000
8580196800000 -25966899200000 54477440000000 -78233600000000
73600000000000 -40960000000000 10240000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "true"
PowerCoef : -30
PowerShift : 11
PolynomialP : [
7669225 -238235500 2480260000 -2610800000
-130540000000 731024000000
]
PolynomialQ : [
243 -32400 1890000 -63360000
1348800000 -19020800000 179840000000 -1126400000000
4480000000000 -10240000000000 10240000000000
]
}}]
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CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -30
PowerShift : 30
PolynomialP : [
-3140790664563 20282405042250 -52494734259000 68041163970000
-44152140150000 11471908500000
]
PolynomialQ : [
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51387246182700000 -71683580685600000 69338113290000000 -45921751200000000
19929037500000000 -5117580000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -30
PowerShift : 24
PolynomialP : [
-59233592601 505946027250 -1732944537000 2974852170000
-2559118050000 882454500000
]
PolynomialQ : [
3515706497843 -58776517301400 442037017372500 -1969339242960000
5755757964300000 -11531303920800000 16037715690000000 -15289754400000000
9562657500000000 -3542940000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -30
PowerShift : 18
PolynomialP : [
-7375554711 94918331250 -491625207000 1280539530000
-1676663550000 882454500000
]
PolynomialQ : [
59797108943 -1505381763600 17040816292500 -114223206240000
502054710300000 -1512007819200000 3159784890000000 -4524465600000000
4248247500000000 -2361960000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -30
PowerShift : 8
PolynomialP : [
-122534073 2685494250 -26604369000 221594130000
-2088475650000 11471908500000
]
PolynomialQ : [
16807 -2881200 208372500 -8255520000
195104700000 -2823854400000 25084890000000 -136468800000000
442867500000000 -787320000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 11
PolynomialP : [
1602480483 1416834587700 -173879632692000 10436702858640000
-313103081469600000 3757237383542400000
]
PolynomialQ : [
714924299 -218112498000 26835230898000 -1677329596800000
54447575198400000 -807728734080000000 3322224927360000000 -6244812288000000000
6096166272000000000 -3023308800000000000 604661760000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 14
PolynomialP : [
-1265122252467 54359524782900 -932194548108000 7990597829520000
-34245622389600000 58706827228800000
]
PolynomialQ : [
7028611650851 -341010807858000 6959010313458000 -77453783971200000
510840122385600000 -2043590186880000000 4956939192960000000 -7292892672000000000
6358186368000000000 -3023308800000000000 604661760000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 16
PolynomialP : [
-757391682951 20709906678900 -226057935996000 1233204529680000
-3363383800800000 3669170140800000
]
PolynomialQ : [
45492921326699 -1519244125938000 21813414268338000 -176133818044800000
879587115422400000 -2821924241280000000 5874793349760000000 -7857243648000000000
6499274112000000000 -3023308800000000000 604661760000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 17
PolynomialP : [
-435930939801 10094402819700 -93267080964000 430575762960000
-993708064800000 917287286400000
]
PolynomialQ : [
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1065214272657600000 -3179682449280000000 6276221573760000000 -8099108352000000000
6559740288000000000 -3023308800000000000 604661760000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 19
PolynomialP : [
-103360140909 1838120123700 -13014363636000 45988022160000
-81193687200000 57323894400000
]
PolynomialQ : [
208730966852651 -5139750209778000 55763828883378000 -350559625507200000
1412458131153600000 -3808194756480000000 6956018156160000000 -8502216192000000000
6660517248000000000 -3023308800000000000 604661760000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 20
PolynomialP : [
-44596750959 712993446900 -4528972764000 14339857680000
-22669567200000 14325724800000
]
PolynomialQ : [
286871423439899 -6628607987058000 67894304401458000 -405659129788800000
1564859339294400000 -4070886698880000000 7231699128960000000 -8663459328000000000
6700828032000000000 -3023308800000000000 604661760000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 22
PolynomialP : [
-6790571523 91652814900 -488178252000 1289707920000
-1695362400000 888796800000
]
PolynomialQ : [
446321492229251 -9440407591218000 89312246200818000 -497626895779200000
1808198102289600000 -4477017847680000000 7649251666560000000 -8905324032000000000
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]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "true"
PowerCoef : -30
PowerShift : 25
PolynomialP : [
-111538323 1325810700 -6151788000 14016240000
-15746400000 6998400000
]
PolynomialQ : [
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1980373989470400000 -4755834103680000000 7930307410560000000 -9066567168000000000
6801604992000000000 -3023308800000000000 604661760000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1762059375
Alternating : "false"
PowerCoef : -60
PowerShift : 15
PolynomialP : [
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14279247817681230 -42049112536556325 85598494996790250 -118944360443668680
107976311014313520 -57826406256512400 13874549065109280
]
PolynomialQ : [
-32 1040 -15680 145480
-928930 4324093 -15159195 40757940
-84738960 136242405 -168022107 156100770
-105763320 49338720 -14171760 1889568
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "false"
PowerCoef : -60
PowerShift : 31
PolynomialP : [
-127657600000 1063540000000 -3544450000000 5906562500000
-4921601562500 1640400390625
]
PolynomialQ : [
248832 -3628800 23760000 -91980000
233137500 -404271875 485703125 -399218750
214843750 -68359375 9765625
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1691577
Alternating : "false"
PowerCoef : -60
PowerShift : 7
PolynomialP : [
-528900000 13171250000 -131456250000 656640625000
-1640800781250 1640400390625
]
PolynomialQ : [
32 -1200 20000 -195000
1231250 -5259375 15390625 -30468750
39062500 -29296875 9765625
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 3123927
CoefficientQ : 0
CoefficientD : 195784375
Alternating : "false"
PowerCoef : -60
PowerShift : 10
PolynomialP : [
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-2374945116006960 2849934139197984
]
PolynomialQ : [
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78602400 -263419776 565937280 -772623360
646652160 -302330880 60466176
]
}}]
[-1 {SeriesBinaryBBP : {
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CoefficientD : 54567
Alternating : "false"
PowerCoef : -60
PowerShift : 42
PolynomialP : [
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-4570317350000 1305713900000
]
PolynomialQ : [
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]
}}]
[-1 {SeriesBinaryBBP : {
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CoefficientD : 54567
Alternating : "false"
PowerCoef : -60
PowerShift : 6
PolynomialP : [
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]
PolynomialQ : [
243 -16200 472500 -7920000
84300000 -594400000 2810000000 -8800000000
17500000000 -20000000000 10000000000
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 51
PolynomialP : [
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-4713026006250 1082722190625
]
PolynomialQ : [
199690286432 -2221828736400 11122707960000 -32991379785000
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21015703125000 -5189853515625 576650390625
]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
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CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 31
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]
PolynomialQ : [
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}}]
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CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 15
PolynomialP : [
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]
PolynomialQ : [
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}}]
[1 {SeriesBinaryBBP : {
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CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 3
PolynomialP : [
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-382137243750 1082722190625
]
PolynomialQ : [
32 -3600 180000 -5265000
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256289062500 -576650390625 576650390625
]
}}]
[-1 {SeriesBinaryBBP : {
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CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 49
PolynomialP : [
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-5334459723450000 1391509586700000
]
PolynomialQ : [
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]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 37
PolynomialP : [
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-16472593350000 5773898700000
]
PolynomialQ : [
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9562657500000000 -3542940000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -60
PowerShift : 25
PolynomialP : [
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-10698694650000 5773898700000
]
PolynomialQ : [
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4248247500000000 -2361960000000000 590490000000000
]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
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Alternating : "false"
PowerCoef : -60
PowerShift : 5
PolynomialP : [
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]
PolynomialQ : [
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442867500000000 -787320000000000 590490000000000
]
}}]
]
}
}
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