Rule: Q[36, 37]

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.

• $P_1$:
  $\frac{110628135069209194801}{17179869184}\cdot t^{36}-\frac{490814965447899948765}{8589934592}\cdot t^{34}+\frac{3990539066902490887785}{17179869184}\cdot t^{32}-\frac{615456273999886654335}{1073741824}\cdot t^{30}+\frac{4118822756768472225165}{4294967296}\cdot t^{28}-\frac{2471293654061083335099}{2147483648}\cdot t^{26}+\frac{4388909494917224502225}{4294967296}\cdot t^{24}-\frac{733256065736776006425}{1073741824}\cdot t^{22}+\frac{2971616687459565920775}{8589934592}\cdot t^{20}-\frac{570310273350825782775}{4294967296}\cdot t^{18}+\frac{329273478576137150055}{8589934592}\cdot t^{16}-\frac{8804103705244308825}{1073741824}\cdot t^{14}+\frac{5450159436579810225}{4294967296}\cdot t^{12}-\frac{294362129962575675}{2147483648}\cdot t^{10}+\frac{42051732851796525}{4294967296}\cdot t^8-\frac{456375395290815}{1073741824}\cdot t^6+\frac{166966608033225}{17179869184}\cdot t^4-\frac{755505013725}{8589934592}\cdot t^2+\frac{2268783825}{17179869184}$
• $P_2$:
  $\frac{110628135069209194801}{17179869184}\cdot t^{73}-\frac{151393823770839056259853}{1288490188800}\cdot t^{71}+\frac{546334473106932067841408437}{531502202880000}\cdot t^{69}-\frac{1643430862905757590882047433629}{286286413824000000}\cdot t^{67}+\frac{30969233831314136397143433123011339}{1347136625049600000000}\cdot t^{65}-\frac{1447150757626617525720756568157233522877}{20583635295928320000000000}\cdot t^{63}+\frac{18740412156416360115638147142746134134356860361}{109754612838092242944000000000000}\cdot t^{61}-\frac{2445806228525995868144679728189918705634458175529}{7233826755237897830400000000000000}\cdot t^{59}+\frac{90981242225495653869559481032971020757102691178019830759}{163592268687029535644712960000000000000000}\cdot t^{57}-\frac{203642149680296068713715947258314051182382472838742354372909}{264350234173813636007706624000000000000000000}\cdot t^{55}+\frac{726327963275638205539032035109506081987883092494948973199673377853}{800148139155904784964321228595200000000000000000000}\cdot t^{53}-\frac{45019139237588816314405277672783135055432482328193140221925261701971}{49099999448203248168265166300160000000000000000000000}\cdot t^{51}+\frac{20928856941539040533867609932840973565004449130829777255582697548110942694177}{26214538092653234926366821981230600448000000000000000000000000}\cdot t^{49}-\frac{1428894667270246501499636915880691174417559471105274847391474554395967278882829}{2374628612938393683265046536611473222400000000000000000000000000}\cdot t^{47}+\frac{304394261127570168758274261940132992160490718642931640973813290170247600981021418969223}{773210584726148909582283975406928344698759720000000000000000000000000000}\cdot t^{45}-\frac{797355320784820785870684062667878686569883167769519345849679223336493784467295338934270155459}{3560481857843753967364750300599222293778723074019000000000000000000000000000000}\cdot t^{43}+\frac{17850812460110517889870629895622297629946489391795940755461798961704306427710632790406311842055858953}{161039882333901423193114183146042704503152888893264566200000000000000000000000000000000}\cdot t^{41}-\frac{623064851663099595439685290899889658688754296320751054678334860755146527597042374556292368321947027837}{13053990461914736577017589088353461652907090236044930745000000000000000000000000000000000}\cdot t^{39}+\frac{9755835795347333903414466470807895936386279424283912787663497025012537386766412412649394770416918565072092309943}{546264514006026994409060178119356222870195207302770265687354946687500000000000000000000000000000000}\cdot t^{37}-\frac{414436096468858209550065912815823570594174692126766190415619623945680695119852924523551516631233374470024437}{71512291147900768372974659220337911683219794770449388406133850000000000000000000000000000000000}\cdot t^{35}+\frac{7540451300154994068791739195410046930722976862099882510875019277852251989893209256215726901425361796846673}{4636826364536346612418811460142230904593796853431544569114293750000000000000000000000000000000}\cdot t^{33}-\frac{1411063954035769679636302788801206215531250908937253861598234663315656142649893145991032378178275502871157}{3589801056415236087033918549787533603556487886527647408346550000000000000000000000000000000000}\cdot t^{31}+\frac{105008895798134826881483271768103663891638413851595781668609594557337571274576274320472618800844264803}{1289440034631909514020804076791499139208508579930907833457812500000000000000000000000000000}\cdot t^{29}-\frac{247105011177799231318943158112650061354907749335017784560510742276319020901435355329798115200111633983}{17192533795092126853610721023886655189446781065745437779437500000000000000000000000000000000}\cdot t^{27}+\frac{4424366821760285553190837815972070932348882591663544086883407340860657634766161395759327703860986507}{2063104055411055222433286522866398622733613727889452533532500000000000000000000000000000000}\cdot t^{25}-\frac{6719782671096095625533065944194012988707403690475999718109723912980854917779018166147633664021523}{25072445117842684994848968159834705484609889054212096761679687500000000000000000000000000}\cdot t^{23}+\frac{8585235524561620631199805395822134345045266079263770022136315781448287846074293971233386233379}{309496557967455028867879766406600453455387597943212201250000000000000000000000000000000}\cdot t^{21}-\frac{29023849361489504616884307562380894833032097577078846416786172959527118758898959705531844375402653}{12378624332466331334599719137198391736401682367336715201195000000000000000000000000000000000}\cdot t^{19}+\frac{8043734056235779930575804287130597606328876666706578761284678068116444947741974462649486033921}{50566275867918020157678591246725456439549356075721875821875000000000000000000000000000000}\cdot t^{17}-\frac{128231897396038420087895302387338707505071038511087720618477551551299880585017671230287592109769}{15129429739681071631177434501020256566713167337855985245905000000000000000000000000000000000}\cdot t^{15}+\frac{978330229318494594524568657521141324614635886356458274652401187148601834654928477341372435239}{2836768076190200930845768968941298106258718875847997233607187500000000000000000000000000000}\cdot t^{13}-\frac{49720069383861269192714720448176045285387388366402430168454882515296807103864792214313010813}{4813909462625795519011001886688263453045098698408722578242500000000000000000000000000000000}\cdot t^{11}+\frac{327806199532289204964001759015273674836949362131573498510314622719457801169239778468066599}{1514488370264295219464135425025521086351267006240946429110000000000000000000000000000000000}\cdot t^9-\frac{852349173759884267576457497748458380054107396570566113555994376578331490122488298808916453}{288834567757547731140660113201295807182705921904523354694550000000000000000000000000000000000}\cdot t^7+\frac{224936908152541067847908089464382521687985921702416958596634654423956992107819847364919}{9627818925251591038022003773376526906090197396817445156485000000000000000000000000000000000}\cdot t^5-\frac{28745958408721758093120413811867678955786269621265810567212737159041177872570087593627}{327345843458554095292748128294801914807066711491793135320490000000000000000000000000000000000}\cdot t^3+\frac{3272917167546241141376922988892724255357428425058884521555256031141930546456589107}{33102388664348166939716102861272103744534835993552114807690000000000000000000000000000000000}\cdot t$

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.