Rule: Q[4, 5, 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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{43}-\frac{122695471448047212375445027146342412790803612788321936}{20059506747419960058056579667371585555506498480433}\cdot t^{41}+\frac{21153288736822286920143107262431779549202694140894318676}{20059506747419960058056579667371585555506498480433}\cdot t^{39}-\frac{2181079380165469439056721936055972495011117155412129854086}{20059506747419960058056579667371585555506498480433}\cdot t^{37}+\frac{150401439024545424137986941881490107856187814350504649784348}{20059506747419960058056579667371585555506498480433}\cdot t^{35}-\frac{14698447451988240151112010271496672452663613958671157767775465}{40119013494839920116113159334743171111012996960866}\cdot t^{33}+\frac{8486928595370068021033693648493508430455596648323888692720495}{647080862819998711550212247334567275984080596143}\cdot t^{31}-\frac{454040833980762622623080628151384721233442936714882080548388245}{1294161725639997423100424494669134551968161192286}\cdot t^{29}+\frac{36702544264378477454387379962532957026844069397845411086870686305}{5176646902559989692401697978676538207872644769144}\cdot t^{27}-\frac{140755463001991737402183745616052639160905629097219834943308115785}{1294161725639997423100424494669134551968161192286}\cdot t^{25}+\frac{26216274323046414990175458407205279907171778676808906038416286958125}{20706587610239958769606791914706152831490579076576}\cdot t^{23}-\frac{460942491476060615073093380512460500747642575825093942370998598639875}{41413175220479917539213583829412305662981158153152}\cdot t^{21}+\frac{3031829784578989550438825137552049469305318591128375385773960255506375}{41413175220479917539213583829412305662981158153152}\cdot t^{19}-\frac{58838771972872479536383427565042301250465151707645965176163423140751125}{165652700881919670156854335317649222651924632612608}\cdot t^{17}+\frac{206408566984943518666886136474731799327700455437827334205111026604040875}{165652700881919670156854335317649222651924632612608}\cdot t^{15}-\frac{1018949641977010177509218893200936070045780258465927257077101609283180625}{331305401763839340313708670635298445303849265225216}\cdot t^{13}+\frac{13642969518169130880219279309759024292472915833167002849463155758984434375}{2650443214110714722509669365082387562430794121801728}\cdot t^{11}-\frac{14717364834653151069140199657438269547776372547869242867117208383216108125}{2650443214110714722509669365082387562430794121801728}\cdot t^9+\frac{38123286340579468912421916378365224863238683289983072327241009523025541875}{10601772856442858890038677460329550249723176487206912}\cdot t^7-\frac{26716644994983363570748602427077799763813671295959198742986804091838373125}{21203545712885717780077354920659100499446352974413824}\cdot t^5+\frac{1070725224047482042589955799865463950501852486614964451982510312951715625}{5300886428221429445019338730164775124861588243603456}\cdot t^3-\frac{863817637993491677133618565073031744825507495853918668437442550713534375}{84814182851542871120309419682636401997785411897655296}\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.