Rule: Q[2, 46]

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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^{48}-\frac{106486910997526021448713606542165670318976254955948614107419379943923541408774305356709539240542879017}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{47}+\frac{4988983929135094733241029918487231895045985202147837733330529550715107525454748114815320877702601399315693}{4216123866521644403419324451280043263324816257208489442646552635681235017673621738537084355600139132}\cdot t^{46}-\frac{847515773009093667276825096261866857339984756834727704297279628646790193887269487556657610525954744176319767}{1054030966630411100854831112820010815831204064302122360661638158920308754418405434634271088900034783}\cdot t^{45}+\frac{826107655947437624785011981930486545496464044946845307100590841028615122685876723293244718306278045753454862525}{2108061933260822201709662225640021631662408128604244721323276317840617508836810869268542177800069566}\cdot t^{44}-\frac{13986975650122601912503521671435976703344913934109953739113817244883528485536300996363995449023716465130091483680}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{43}+\frac{4143354390039026534368322145730157486248553655646155100895230349452727454069629940091482300048910790235740107618890}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{42}-\frac{1002882336639804556772614588963409768161722109306846080175682915550530190164006782946374793778554590068345227806826040}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{41}+\frac{202239354634058323556591123081341943644483711401221106533159933062142232481276361922288973291718778440791135465858458540}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{40}-\frac{34475189498135055418460561391261659104283706390454685090451105981387969173930901287075561645873757389725880129320722576000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{39}+\frac{5023529322757523315112388377754758933390046003314868566223497565223043859053582237365550641383084088573464742466875612215200}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{38}-\frac{631173863635575171962852513751612914341333950849877720775309615678810153668986883820719593033888307692987542286258246448713600}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{37}+\frac{68851128239475349826925528682228595369746483741992217896558420423494783923682076216637091962830138816763328527175807140649601600}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{36}-\frac{6556429830952863199775002457605428578568996739102363310177596709139717756476052691874655547508928655300912684096045939359003801600}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{35}+\frac{547399292584903802811857857070358517927577076307959448856007185029531711666250326727320290859882349368541896420537263540995099040000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{34}-\frac{40207894510910359237379382094564553602754833714622269379575064146183039587670390321549826137336034167243943068338987661499843240832000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{33}+\frac{2605239128572336076727100049519440177255480973945495215312416524964813526160769881274920053092671238425510121506351161889688990177216000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{32}-\frac{149206967996580105967620588586672236123277958321333074043610259729489037339914720156157260650772848640764324179850636218809306144751616000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{31}+\frac{7564232560905588419814992774932094388154763345407422660673780593159722257477880949847100236035287307475037423045714239138338002543087616000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{30}-\frac{339768548026369957402397474194515179919324205099358903112747058845450786548917370717203938398134998931818150802992583526740911656948121600000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{29}+\frac{13528534336268365616530710505897425915692346713406101820209986692547977626574338327629256315228510281386098939097698304852236793419087093760000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{28}-\frac{477514149806132774857961431764868143795604189010765836332818178303865226853194561271047301209396388492548679961001430039268102114589493166080000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{27}+\frac{14935815677642086679171303090436834150641527775454412288073554305620908399353398784728847250508074808369518741343286683911176637165426217287680000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{26}-\frac{413659869971758383876245570757779617817387487859056507521873060882002420008740838345349735195172545374060315384131445608717299647136824893767680000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{25}+\frac{10132586741627107183966194373087211180254690078517949552334060907657856950030830296926251817914146701163695563078516369900942945850790754099200000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{24}-\frac{219166492190867094842496133507314286947045989894959377954595024974047605360733939670870412946657635801329408823717278913356525923416757928984576000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{23}+\frac{4177696175902025479668210507837198177846221704907579702079118876189367712538300406658898277931075967179638183226518932107232585529280828543664128000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{22}-\frac{70008095220217047418367091446171608575492498940583942630453503906835295919005370487033582156160205044714729450170625771444698737848412075790696448000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{21}+\frac{1028353273942092256885195707458729358201838321274399278608295277554633436072890634286983374908361937367400231812075341715618900994701773008916840448000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{20}-\frac{13195589098860135272148048067916531332764289428499032861006377045196285888077907524073227333090435473192840128459096127968322127841859343050132684800000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{19}+\frac{147322574155776475578481886521794288480843985799275193444774912134629953895035095326559918089452953991039607680513618680335245399670243567452325150720000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{18}-\frac{1424449895817437275135069381253155080161488719944865144702724370223993066784788631452474410187517643016355003044633407886251480154133425740507837890560000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{17}+\frac{11863933903185662512430195579793979952636933389458468676445950036972873306184344396782708854662273538759240054780836833466818924948285697896538476380160000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{16}-\frac{84589043985497994607653819838753198402654849621671118673102389709945021827138620240664330941067692355049147143458310939513924745157201016574273818460160000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{15}+\frac{512595376212759552818907426780498245368521495311603947796660233324985781846974242583175641538492564713218309927115481405556491482614164097934293991424000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{14}-\frac{2618013348057557860486652256126516872258365481570479578769643748297753996816645563994286541279009319172575501067088235927154885535734159970102319828172800000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{13}+\frac{11159671721582557198092883284033106937369784352234128608836682047776298090783201684434147434355818629928808342802472548158568113648581089869998399579750400000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{12}-\frac{39246707298755673828660831299945409126239368005184294001395840604502212038759232881567791744216221670962738432073015263597458686116279297665185603806822400000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{11}+\frac{112323744890995752553626342893821335865983532680075981306314559881557355629281706213422416897851044175036881843161715728257721332766733901970868317611622400000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^{10}-\frac{257331491952961858879568675415917970574695830543563652656486169934336240444872681412005924161621284012628267677487928320984228363050686182782337296629760000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^9+\frac{462512021967228414344053045407468775593132948303481264998092733056938744223336975302469270743230283313314621608000196202791086421352136754764180281622528000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^8-\frac{636045575670268956310563395152222222042713122409060695481378354751102792111410094311642397169457185877606583390116541768587662339669485092214820793483264000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^7+\frac{648252896861274719026554847706284884906379566436761724967456843807331988224990621840557636111479533023499110954289135524388817459828200695179019512971264000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^6-\frac{469588598092470224223499122145391684677897955108639254460562444805286650190041812767488365673294697408127144863615862007131174342587212869357374237835264000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^5+\frac{228323605590146477735295002654203132655309119648847076362911035256824001253906324647393699166654706738503887509620960842582069540148297554714450880102400000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^4-\frac{68587110858652042589363237788494281283731316456580683537003582061974606277994646404502425120768296176215592798366481699121019529036101675836092805283840000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^3+\frac{11168322404248207677201011434400759736018808408812246711023532500773866671843356432257337830702254705360797307057685454159880916078668445321385444638720000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t^2-\frac{777080548549706268813831944775965353204142828796895901912055656346560657208192365590392191876895863358337581588996598508896691329058376284667767685120000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}\cdot t+\frac{12954502598479973740832487688998285083391299899294742933324969172715308412374828507316918924544794892140560258938318189184458615962720735960624005120000000000}{95820996966401009168621010256364619621018551300192941878330741720028068583491403148570098990912253}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.