Rule: Q[4, 10, 30]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{44}-\frac{12026017565094668871888288986841923322400312513922260069510583619554397090340542655454532457889525873705}{233625519930155436555004821176593861195407735922336638200224761260247676239816383598475432138425580868}\cdot t^{42}+\frac{4530409694865612769566614513536650763433105664390712679928702892594501034935713346405976201634946773297458743}{16023439909929640771561560665217866563948234975969380667600615475795347122584046485485035988646056889412648}\cdot t^{40}-\frac{2779448644875068891274149160849110532849412692101949183354603205696476571340461760477074057298988297226444364735}{2886889757105656945676341179850085625938007001503816750279377554889128373252225708468220650621064582909178748}\cdot t^{38}+\frac{44913429120790759982459613731918234740984951323109493005273824427922006502505413136782149248962038027094011393771605}{19729004600060059566752115623095485167660339848277083671409266210112303302805710491671819926344355359601327563832}\cdot t^{36}-\frac{159334306244791519569127278554615298217518172104726407589669500807271709596896964136169319968061160138374409681538905}{40162616507265121260888235375587237662737120405421206045368863356300046009283053500903347707201009124902702540658}\cdot t^{34}+\frac{49879178214894038714447026524936360488022413052660522387203234516150751386230411102702803051432553139474653924330655}{9450027413474146179032525970726408861820498918922636716557379613247069649243071411977258284047296264682988833096}\cdot t^{32}-\frac{394852631528129254167959928191333572808774310360102011529934740844984013845470615883542692528971279984962234007976569}{72056459027740364615123010526788867571381304256785104963750019551008906075478419516326594415860634018207789852357}\cdot t^{30}+\frac{9979810844083628351480231910158129109701492645977893215816251158239500398553723131185288399236295038350888649513247185}{2218085782245225136848134410998544271327737539730602361492826688787578500062553087719966471583883864560483270237772}\cdot t^{28}-\frac{846366069596426673985587384065851783993358214374524872252624711510288630025741780183597516301168081444591575545597485}{287529638439195851072906312536848331468410421816929935749070126324315731489590215074810468538651612072655238734526}\cdot t^{26}+\frac{16812923386542085023128862164782143484143486228075269931720140043972198191545641014040560864778226862875669152957848575}{10926126260689442340770439876400236595799596029043337558464664800323997796604428172842797804468761258760899071911988}\cdot t^{24}-\frac{10521303200740061942591990127605038984224451146888810840537734047858973531174534409557537120786408405684577593263905025}{16389189391034163511155659814600354893699394043565006337696997200485996694906642259264196706703141888141348607867982}\cdot t^{22}+\frac{5642559692192579801415151107990364932327437476189628020926328999648441215342782586524861192225377065858347137383989805}{26534878061674359970442496842686288875513304641962391213414185943643994648896468419761080382281277342705040603214828}\cdot t^{20}-\frac{19347248695445590555699173711044638637918813605573655007668877394123566542279696869919271323071362162931034711742550}{349143132390452104874243379509030116783069797920557779123870867679526245380216689733698426082648386088224218463353}\cdot t^{18}+\frac{6877603195436853863301056260469442018561735415409334022289823155093479162887608882260922726832179651175771061841892475}{613916853730317312876522535310819308875266023496547831386514586863317560406202193501159608968383856291129314018032228}\cdot t^{16}-\frac{1850680998059633671932337746819585483057569234509792941664333540186016650245764657391380219584014560897163686324954375}{1074354494028055297533914436793933790531715541118958704926400527010805730710853838627029315694671748509476299531556399}\cdot t^{14}+\frac{11789367756984429058276683163424320966725578127269526566209838571754127334913404461099124610992127722473791884198217375}{60163851665571096661899208460460292269776070302661687475878429512605120919807814963113641678901617916530672773767158344}\cdot t^{12}-\frac{1431297490791047233282463418074920988721972841601968646191331877608759161215259897423881369385900044655513781527711715}{90245777498356644992848812690690438404664105453992531213817644268907681379711722444670462518352426874796009160650737516}\cdot t^{10}+\frac{17310006072251814542795817734673805523121529847378614653625576830612949554999407764123696149798268198545833396801725}{20054617221857032220633069486820097423258690100887229158626143170868373639935938321037880559633872638843557591255719448}\cdot t^8-\frac{41500591718557070950074871151951380378836893328380936931135589381021245869406543525783473260434973390948483348925}{1432472658704073730045219249058578387375620721491944939901867369347740974281138451502705754259562331345968399375408532}\cdot t^6+\frac{4459885358122062600255073440549095164609435341010010615223345403685928988863925936414012885249430830467099334625}{8594835952224442380271315494351470324253724328951669639411204216086445845686830709016234525557373988075810396252451192}\cdot t^4-\frac{1969959435620274234114421750169924233928078192974521674899567516691860061046964444470135440055048758276089125}{529392069521070726321059287695561577943164179681805738659385766932860794843029427729260822226359992019162234551781414}\cdot t^2+\frac{71227272556373853876983661277545544244681966232170987544127160006579224726274985547056355961022419010325}{15921566000633706054768700381821400840395915178400172591259722313770249468963291059526641269965714045689089760955832}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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