Rule: Q[1, 45]

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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^{46}+\frac{88230459261614823129940381745138026466819268161489937128969}{42591665236474640562684440473669440358639278611408414744}\cdot t^{45}-\frac{87416166818884923164605993541091411098942295566005164517879425}{42591665236474640562684440473669440358639278611408414744}\cdot t^{44}+\frac{626992619992822144674413904145024182935020602202346296412970075}{483996195869030006394141369018970913166355438766004713}\cdot t^{43}-\frac{283328441028480664044008770610031822066528655149905977512265896825}{483996195869030006394141369018970913166355438766004713}\cdot t^{42}+\frac{97665462934550534116088755109440448853570176229531059490294113622585}{483996195869030006394141369018970913166355438766004713}\cdot t^{41}-\frac{26720237966769907369745915668003211458793010192029443780345406079827685}{483996195869030006394141369018970913166355438766004713}\cdot t^{40}+\frac{5960655710790835831916411073412157827911034516667109118512779731747308000}{483996195869030006394141369018970913166355438766004713}\cdot t^{39}-\frac{1105354135529443064818114232635462024668194632046188699745759845927830756000}{483996195869030006394141369018970913166355438766004713}\cdot t^{38}+\frac{172869038248962234053607383283455979009792969514038499323855181232867045706000}{483996195869030006394141369018970913166355438766004713}\cdot t^{37}-\frac{23052611029638280678513460796497400308470479456991969065420338501730227776880400}{483996195869030006394141369018970913166355438766004713}\cdot t^{36}+\frac{2643775285181795131232194525877329228117126418019603597739341262701320024327798400}{483996195869030006394141369018970913166355438766004713}\cdot t^{35}-\frac{262510747462088215011361152362687499757794119543241415687984224427679280583779120000}{483996195869030006394141369018970913166355438766004713}\cdot t^{34}+\frac{22687487155398944563700597070868692777843444436218776808261238207757658167088285840000}{483996195869030006394141369018970913166355438766004713}\cdot t^{33}-\frac{1713752370933528878627782046888058664103123040549585275836023990274921592772019404240000}{483996195869030006394141369018970913166355438766004713}\cdot t^{32}+\frac{113509877632777059823947323015019940131673888399097367304348931995792895286405607809024000}{483996195869030006394141369018970913166355438766004713}\cdot t^{31}-\frac{6608532329177626967943465043059059636517427211544125060433660822803369703489454875500544000}{483996195869030006394141369018970913166355438766004713}\cdot t^{30}+\frac{338790580572524917775881446927978570999327785353277532202051619167557986497367978751436800000}{483996195869030006394141369018970913166355438766004713}\cdot t^{29}-\frac{15311698499791606689042958831265415098937052411679312083474595168945367769067227415530137600000}{483996195869030006394141369018970913166355438766004713}\cdot t^{28}+\frac{610461526026629935103882144182321557998299964799021880268296641110817856330505362555658649600000}{483996195869030006394141369018970913166355438766004713}\cdot t^{27}-\frac{21473206000560017741102333261980425041270574836055149516451624546246096165279085961459008389120000}{483996195869030006394141369018970913166355438766004713}\cdot t^{26}+\frac{666184781864560812334460845767442619162290780271700152955033975725045136757257427878506623057920000}{483996195869030006394141369018970913166355438766004713}\cdot t^{25}-\frac{18214114694173406554467232463655063145180335744369758321144654744574587034735051218818977945600000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{24}+\frac{438324113315986014379469634550582168879497526101768971990667783765774870702989059394240697139200000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{23}-\frac{9268596684162663049162374069833902421964970611427542255316755382002736840316352762174701572915200000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{22}+\frac{171835475815825321300797311730980608126431947752820235271527073917389412464865000932964759682056192000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{21}-\frac{2785609063206973665872564542625376831744512708867916705528219144803452896470445648618855305323118592000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{20}+\frac{39357393989734281442576491021741964140716907066745267767933878024051749127896130095010266015393382400000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{19}-\frac{482792446704752758055010312199382849808502316400271266653211869961965872022321175147575951872249036800000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{18}+\frac{5118704337925804861453929074727309523609179446566167934664110910572315267213980839217779946484747468800000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{17}-\frac{46658584566282887166036567307445689321917405729754375398275494743970703582021472725114949003985547427840000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{16}+\frac{363412513119357419355391596965312387301021311649758965203572061999578316441172755536642349613430593290240000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{15}-\frac{2401280329634215422625006553182697679341537023669642683114074362541738899223712813275745679917126254592000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{14}+\frac{13347697562848424306662228008478677471292803580641692662410436429490690337884976335762335408075892588544000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{13}-\frac{61800542760434557092227962690684037953913421360467197612348849153036186034654868825443216791536199532544000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{12}+\frac{235564156992181453042154815002387398910368532792603837300587857107936885368547639858510743135955919149465600000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{11}-\frac{728901391004734273406405762815668723382407951562360357728899049255335645717279424751637607131603090905497600000000}{483996195869030006394141369018970913166355438766004713}\cdot t^{10}+\frac{1800122909631149539576612785843789250403812315659525633867087149874159411565304366309167251803660384993280000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^9-\frac{3474989653762989136294687311195416861680616367288817746653796641093522604987532739095934487585458969640960000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^8+\frac{5108308038040013458685693927017749083077702406284634705639060106161438300340635228080905745118419023298560000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^7-\frac{5529734466146280453638835116123724177751644659616757302209090679025468137603208443538699490240127037341696000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^6+\frac{4216207245974819491072122589742083078887603399396442322935901907514982362497780350644351705794313847832576000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^5-\frac{2129189218766973024635830258106805198457088719574695232305701102951679744063624924295058917341596431155200000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^4+\frac{650690704115661101152661589700284028334045337402997487843024097099149851064451693241870710182380988006400000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^3-\frac{104139195287038888342812110602875205788969511380107791827949097425845719650488172024693153057068181094400000000000}{483996195869030006394141369018970913166355438766004713}\cdot t^2+\frac{6682894642865600532916184698485781524086684777419208667216775150670857918510896765648810257334486958080000000000}{483996195869030006394141369018970913166355438766004713}\cdot t-\frac{89325476671376084343578831136337929474359219539757300839475059834296779741076338555372130884942561280000000000}{483996195869030006394141369018970913166355438766004713}$

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.