Rule: Q[2, 6, 48]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{56}-\frac{2976930421163427840748804646515588513877183024307742174159341992991906915211106709291035}{137252649418551080131850141969220036795982588885563267817015507855081233962891238552892}\cdot t^{54}+\frac{48454852357605181053647321562055381495892047853077203490048301953090466936916869071461283965}{326161498798457601686153393030138791968747530610755413051880229581583324036306845698511108}\cdot t^{52}-\frac{176943907845092678665877316330648752407427326176674125845698704677802097124005861115050793025}{275982806675617970657514409487040516281247910516793041813129425030570504953798100206432476}\cdot t^{50}+\frac{5417373817841704531472290922647736800899639643284645558747552079097548881252336890733806911525}{2769344715262235498666782522783751387511832481392647419573126299444690239363974040002477604}\cdot t^{48}-\frac{1141428392721102464348869890889849273033857941329912870371793954647307335807029866537943510189255}{254318156351581959960899528342307835753169949541224788030798765165670720314924949340227526634}\cdot t^{46}+\frac{2044971592887214719614097876584509786597005927181820761794369791839383551542439194211598281365575}{254318156351581959960899528342307835753169949541224788030798765165670720314924949340227526634}\cdot t^{44}-\frac{80600968936660940561953785341131136907844597751614138796375323056595087392112599754614075136925}{6989716770762294882646287248308672018586066266460723561100177478126256583708296704911115954}\cdot t^{42}+\frac{129804254209849075135057430350488678552165164873580794720699195049346861078945158630199975850167650}{9642314285266585790610553259041813049639478414582568152537694831075170957225595304424884458543}\cdot t^{40}-\frac{1113584047805748529185153426191147624671189378333238640819453775252615601675765093105186174418230025}{86039112083917227054678782926834639519859961237813685053413276954209217772166850408714353630076}\cdot t^{38}+\frac{46770626990226236859503694011916688183577660935025103042930944058846982893317560321028467886751835}{4528374320206169844983093838254454711571576907253351844916488260747853566956150021511281770004}\cdot t^{36}-\frac{29032014381968579342644057725928489078145759460182032095094427861403871912318533895454122560189075}{4223090658169798844197716725563143157982481834854249473349084557776088157947870244780184122588}\cdot t^{34}+\frac{12942822483714228172880668014548908199212225389477832867884022367907371984997625321659862557848897125}{3382695617194008874202371097176077669543967949718253828152616730778646614516244066068927482192988}\cdot t^{32}-\frac{11517652772850644220620530740760572150133315682831856207766492823667662759273076343483443096047584925}{6465313397378871799886789919602664578080003258735694816711049719310800384196369706922063010320469}\cdot t^{30}+\frac{7362417651704236756120905603557099068478212755215124422854778449209186826366746575114180948540168725}{10626894434772168590618516764404379708798166275852923664249196665074074194713573196435115062940541}\cdot t^{28}-\frac{264823263870618520166183519359529810225536475603754631444525912169710699071944830381318726640528715}{1180766048308018732290946307156042189866462919539213740472132962786008243857063688492790562548949}\cdot t^{26}+\frac{2391297461198350444242348327828395890965970632186298374735098619677833692509304337902125496235284725}{39782733012224015749494960194949729166270058366013509102061095207713200831491838119987866645879974}\cdot t^{24}-\frac{24921457325347090028020812134163788674961107599146449794302150146445169099411518348155918548786790325}{1883049362578603412142761449227620513870116095991306097497558506498424839357280337679425687904985436}\cdot t^{22}+\frac{405605813137957392521542225224587886222457594060503106700159667510097843983994722920121769617817975}{171186305688963946558432859020692773988192372362846008863414409681674985396116394334493244354998676}\cdot t^{20}-\frac{11708947010213614688643329894202925133458994160437529209321451084903272915065505367528870596697306925}{34408447443481753258245004663159247571626666844932047781546296346016672064619395261233142115354733876}\cdot t^{18}+\frac{5744298244814147059876507302825863463189249553988834803467388426575243064373499830572768621107267465}{149103272255087597452395020207023406143715556328038873720033950832738912280017379465343615833203846796}\cdot t^{16}-\frac{751540203254302357094533600242957314563546375785241009024884418902940322600134039419690522632288875}{223654908382631396178592530310535109215573334492058310580050926249108368420026069198015423749805770194}\cdot t^{14}+\frac{11305040929092704877811991878352171928766247206804648144639713379667865285029476223719729903045925}{51612671165222629887367506994738871357440000267398071672319444519025008096929092891849713173032100814}\cdot t^{12}-\frac{633865862843539802161170329494420292554352119858863116493663229184776352056515763138566649500283175}{61918001174545414988211885891355066005142186987455219982892560274657001380282601772589039236580843609862}\cdot t^{10}+\frac{946664276797973189985237102395978637178260013220386450172123454964666670996158594728004117616925}{2926472692329260907403049333173498144521645653635943233022285187110654294092958790246745635559791115889}\cdot t^8-\frac{163713850067109025900901499781756935441710454117012866457453896615892717361316709539146121195325683}{25881724490959983465072568302586417590149434160756281952849090194806626576958127540942218400890792628922316}\cdot t^6+\frac{30220705817137423575602331507598863032405900095518422857613925036235312282858561557505711507175485}{457243799340293041216282040012360044092640003506694314500333926774917069526260253223312525082404003110960916}\cdot t^4-\frac{1642560086120482054429993759895672270994246059295484033967180634285502649742353904356754760387955}{5944169391423809535811666520160680573204320045587026088504341048073921903841383291903062826071252040442491908}\cdot t^2+\frac{118788953458557267363663266215721828819619550838057661107778703317855044984714623779758342275}{614914074974876848532241364154553162745274487474519940190104246352474679707729306058937533731508831769912956}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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