Rule: Q[5, 12, 34]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{17}-\frac{104576}{53}\cdot t^{15}+\frac{2468820}{53}\cdot t^{13}-\frac{28579980}{53}\cdot t^{11}+\frac{172854825}{53}\cdot t^9-\frac{539111430}{53}\cdot t^7+\frac{3204996795}{212}\cdot t^5-\frac{1892565675}{212}\cdot t^3+\frac{1129052925}{848}\cdot t$
• $P_3$:
  $32\cdot t^{51}-\frac{5675142540107039552565468684783340522082322071812082567132514142541514684043932650857340521338832}{361947278787276079606380737395009697201726430023372024265004165160073849850080265365484966647}\cdot t^{49}+\frac{149287947580999533805404025740970890700473283427937666613540028230659951319710212200800337170996484876}{42347831618111301313946546275216134572601992312734526839005487323728640432459391047761741097699}\cdot t^{47}-\frac{20464640740634449442293618429777756442308126140351612075642140018346993028933563567917268604592690368070}{42347831618111301313946546275216134572601992312734526839005487323728640432459391047761741097699}\cdot t^{45}+\frac{638987315580134318602311874719572080010883069339617741700959063140321335276138979037371627195925535697055}{14115943872703767104648848758405378190867330770911508946335162441242880144153130349253913699233}\cdot t^{43}-\frac{65952669946675402033554793565451275740381048501295372894087538678844184814998134728852403033214868962107991165}{21428002798764318464856952415259364093736608110243670580536776585806692058824451870167440995435694}\cdot t^{41}+\frac{6750447333553301089186055254357449690277569309657451435503214077385371566169921146745701240042008937541585153665}{42856005597528636929713904830518728187473216220487341161073553171613384117648903740334881990871388}\cdot t^{39}-\frac{197766103829307963551215226102760017653352691632560366792156085202205360523719100280528162412794365583267091795}{31851360533280295005361504890760853353751925842056738135320366534086498786807063352162677064936}\cdot t^{37}+\frac{2523394053217598097456913507765128689886756900999495973929219978872271991570410389462236396335928403123884174705225}{13186463260778042132219663024774993288453297298611489588022631745111810497738124227795348304883504}\cdot t^{35}-\frac{11160111960381113571174483775056913412210396340051286482081352546180262016466279763889397906355527526057831920922075}{2397538774686916751312666004504544234264235872474816288731387590020329181406931677780972419069728}\cdot t^{33}+\frac{71795152406092846133846978118838515346907084928227981984181473784335227708334157023030038078114629045363579615037375}{799179591562305583770888668168181411421411957491605429577129196673443060468977225926990806356576}\cdot t^{31}-\frac{2203020059703572222501315036983886923939524097340230658668252787438330865855475011845440955339781571895709501618923375}{1598359183124611167541777336336362822842823914983210859154258393346886120937954451853981612713152}\cdot t^{29}+\frac{53688031276435117347878917711835536445617092199030614640048881178985073030049195506079560463260779771297010893020807625}{3196718366249222335083554672672725645685647829966421718308516786693772241875908903707963225426304}\cdot t^{27}-\frac{38346731162749672770576812670817877254662578513519509323176161610448756524325710856679034235414118517636347003495150375}{236793953055497950746929975753535233013751691108623830985816058273612758657474733607997275957504}\cdot t^{25}+\frac{25282469009710782895435774258476188029444273259276235159129492556476604920598775515212741206315654675281493244309015625}{20590778526565039195385215282916107218587103574662941824853570284661979013693455096347589213696}\cdot t^{23}-\frac{298703427390338629770826801652916819794278231946966846478700781601851111593028188879845578051073428610462413630276520625}{41181557053130078390770430565832214437174207149325883649707140569323958027386910192695178427392}\cdot t^{21}+\frac{226286306842198412192193997605824242780029209485006998835897732173593853636522764578887136018178124225982186291958268125}{6863592842188346398461738427638702406195701191554313941617856761553993004564485032115863071232}\cdot t^{19}-\frac{3114133253770952543716488404596856389245548645797950527083518127730505464193940482261210374525837327739768326755381736875}{27454371368753385593846953710554809624782804766217255766471427046215972018257940128463452284928}\cdot t^{17}+\frac{63504972849781442462809123110125771853169606491706965755185662594051782620480169757264963832047554590030736312583244515625}{219634970950027084750775629684438476998262438129738046131771416369727776146063521027707618279424}\cdot t^{15}-\frac{77749119371633040371441984733476231509086055001312426492522199306165984131948835035316114265440878636430042650500552571875}{146423313966684723167183753122958984665508292086492030754514277579818517430709014018471745519616}\cdot t^{13}+\frac{198202775119120067346020611038100050418432821581832124086762158018332215746161766728135670042876189141606308455467398278125}{292846627933369446334367506245917969331016584172984061509028555159637034861418028036943491039232}\cdot t^{11}-\frac{333260299449137705786273694957357432298545064688873198121098046259414702081963354388716386352714774068669298295467902340625}{585693255866738892668735012491835938662033168345968123018057110319274069722836056073886982078464}\cdot t^9+\frac{343799035553830506326843076746090901585877881045553832538321708972669868247874505092234407935562655509649599231626142428125}{1171386511733477785337470024983671877324066336691936246036114220638548139445672112147773964156928}\cdot t^7-\frac{195441984601232991153874180297031047863381298236607370328457942037008319939633541146253022889590943324773095040543785703125}{2342773023466955570674940049967343754648132673383872492072228441277096278891344224295547928313856}\cdot t^5+\frac{51560998543633382826717179703722561934567634865412661772416994527114867396403421548903382124570800130780467216865153453125}{4685546046933911141349880099934687509296265346767744984144456882554192557782688448591095856627712}\cdot t^3-\frac{4414983813377993531404338743133537642138401133764684337047409149473624080545938214303116635706852445978240064237895078125}{9371092093867822282699760199869375018592530693535489968288913765108385115565376897182191713255424}\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.