Rule: Q[4, 15, 24]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{19}-\frac{748536}{667}\cdot t^{17}+\frac{226304664}{7337}\cdot t^{15}-\frac{3155515020}{7337}\cdot t^{13}+\frac{24226003620}{7337}\cdot t^{11}-\frac{9496214910}{667}\cdot t^9+\frac{1965071745}{58}\cdot t^7-\frac{112008278655}{2668}\cdot t^5+\frac{250467132825}{10672}\cdot t^3-\frac{83438061525}{21344}\cdot t$
• $P_3$:
  $16\cdot t^{43}-\frac{11450711464002921106122836876990392775929972984031283176404763790152761409043531921336}{2166156199411436844482862922643225214273207607239388809008659576754806168958898563}\cdot t^{41}+\frac{131153084696916679457200626998570279279033351255164065795518198534458694220636850414085832}{166794027354680637025180445043528341499036985757432938293666787410120075009835189351}\cdot t^{39}-\frac{11652912509576111009745007295142827976711815905574998635211313057035388660258681900524701612}{166794027354680637025180445043528341499036985757432938293666787410120075009835189351}\cdot t^{37}+\frac{691932055625438372856373168390980063164984895747597051932212714449170119276341867032035248021}{166794027354680637025180445043528341499036985757432938293666787410120075009835189351}\cdot t^{35}-\frac{8317628296930171270984692189004457351063592014243674920571558678699961281967779632825756829635}{47655436387051610578622984298150954714010567359266553798190510688605735717095768386}\cdot t^{33}+\frac{507033919162836808151841042533665328069897432976918443025236426938267495307402416809081127005}{94180704322236384542733170549705444098835113358234296043854764206730702998212981}\cdot t^{31}-\frac{538427529436110721809201944413054524528252897727453222727723031962314738188688231252314580689735}{4332312398822873688965725845286450428546415214478777618017319153509612337917797126}\cdot t^{29}+\frac{37662755626860352468407505929525704815435116881161158764455063878014109193023377899197108842950365}{17329249595291494755862903381145801714185660857915110472069276614038449351671188504}\cdot t^{27}-\frac{1003819409081457181266998518410457027052944129648204797552152057495434828909118088165590881474231665}{34658499190582989511725806762291603428371321715830220944138553228076898703342377008}\cdot t^{25}+\frac{55464797447470690196391039780721808699105065385132608635531781359393521382247749383695841275641375}{188361408644472769085466341099410888197670226716468592087709528413461405996425962}\cdot t^{23}-\frac{3430358168117857528127739072312869660156932035448059183200848042373667532498786542347836046865914625}{1506891269155782152683730728795287105581361813731748736701676227307691247971407696}\cdot t^{21}+\frac{160110629786372521730576703153419573432921513928086484473739280544040736047651098927406544835865995625}{12055130153246257221469845830362296844650894509853989893613409818461529983771261568}\cdot t^{19}-\frac{1392653283686175511076734388651762436909389663094253827612354813408745530731976073849728839061049625625}{24110260306492514442939691660724593689301789019707979787226819636923059967542523136}\cdot t^{17}+\frac{4434196158984583741735256766895060623010324710725257584967256807714487004823402316205993223944692661875}{24110260306492514442939691660724593689301789019707979787226819636923059967542523136}\cdot t^{15}-\frac{20155967072593728208687411478970970163461367604737049422139585825332373327157399418061299500359192204375}{48220520612985028885879383321449187378603578039415959574453639273846119935085046272}\cdot t^{13}+\frac{252537746840512392526138933700580378685839741194736969220298405048598644507041831852651348034621163223125}{385764164903880231087035066571593499028828624315327676595629114190768959480680370176}\cdot t^{11}-\frac{518747662727509553446889293841802271336917439433994539887540069143728887370592831302543697136735504880625}{771528329807760462174070133143186998057657248630655353191258228381537918961360740352}\cdot t^9+\frac{325469971083886701603858744593877408739738234923911807729163200404629953150999048230085889604812562393125}{771528329807760462174070133143186998057657248630655353191258228381537918961360740352}\cdot t^7-\frac{224579488440968862437042314533602499344052136160224074933020006891748864197915396202178807766808048136875}{1543056659615520924348140266286373996115314497261310706382516456763075837922721480704}\cdot t^5+\frac{143900017280366473130504264901414128649710828185688406354676523458370093473575406159627920616298181759375}{6172226638462083697392561065145495984461257989045242825530065827052303351690885922816}\cdot t^3-\frac{14826843405512240548442195574920115672724443279500976391303472235554124322313332372759857956701238559375}{12344453276924167394785122130290991968922515978090485651060131654104606703381771845632}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.