Rule: Q[7, 50]

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.

• $P_1$:
  $128\cdot t^7-1344\cdot t^5+3360\cdot t^3-1680\cdot t$
• $P_2$:
  $128\cdot t^{57}-\frac{303564950838653579647621640612233162731887166026528}{3268268753431485481935020806236322653310270487}\cdot t^{55}+\frac{306632745067584025364396523065573044516775971185224560}{9804806260294456445805062418708967959930811461}\cdot t^{53}-\frac{233548890140712917189920758193204545455044572380478234360}{35950956287746340301285228868599549186412975357}\cdot t^{51}+\frac{33569942176550358892971014757214546335067196578866213410500}{35950956287746340301285228868599549186412975357}\cdot t^{49}-\frac{154346772561964360886707911501329037684445363132830484125100}{1563085055988971317447183863852154312452738059}\cdot t^{47}+\frac{12464578326283950209707328167952627361307556835763651376837550}{1563085055988971317447183863852154312452738059}\cdot t^{45}-\frac{71606301945491080220021565020310287064749256622190228384318625}{142098641453542847040653078532014028404794369}\cdot t^{43}+\frac{3599656570306310632377806704825866198811903619507728718059758375}{142098641453542847040653078532014028404794369}\cdot t^{41}-\frac{1164615220822154136272980955265146437853463023273457814909947283125}{1136789131628342776325224628256112227238354952}\cdot t^{39}+\frac{76350574765417696626481465593316954144812062190239006964438656243625}{2273578263256685552650449256512224454476709904}\cdot t^{37}-\frac{4075795438051680668407164136075323112750092012976863036776450275208625}{4547156526513371105300898513024448908953419808}\cdot t^{35}+\frac{177572033272013828746858248207215732055908875045185019593674784824251875}{9094313053026742210601797026048897817906839616}\cdot t^{33}-\frac{1578924008774010257519292571038189597315651108178973480180544377385166875}{4547156526513371105300898513024448908953419808}\cdot t^{31}+\frac{45774090060342018023626818345777751425327165639476274922287728414354934375}{9094313053026742210601797026048897817906839616}\cdot t^{29}-\frac{1078067064943861775502857579497319724899484431503719090083224690073349301875}{18188626106053484421203594052097795635813679232}\cdot t^{27}+\frac{41042193613416579476634872922767410951468304119791546274719557848181014625625}{72754504424213937684814376208391182543254716928}\cdot t^{25}-\frac{1253831142573620794499997880842264349103064464633169632934147336259223339015625}{291018017696855750739257504833564730173018867712}\cdot t^{23}+\frac{15224374409652672275660689882277440055572248428813870234892569684654184013078125}{582036035393711501478515009667129460346037735424}\cdot t^{21}-\frac{145162176967367365062133128144079667183732984849799779612438010781117651206328125}{1164072070787423002957030019334258920692075470848}\cdot t^{19}+\frac{1069897128374408161656526914555902583678039725188314016773491188760092606272796875}{2328144141574846005914060038668517841384150941696}\cdot t^{17}-\frac{2986110380104523241970389556185864412846849952632336545894968388094105195570265625}{2328144141574846005914060038668517841384150941696}\cdot t^{15}+\frac{12289220988841566935170670729354818350881215751686497352013437423810562783181328125}{4656288283149692011828120077337035682768301883392}\cdot t^{13}-\frac{35959472704321700716862604579546944218336349629341403221880561259262241830873515625}{9312576566299384023656240154674071365536603766784}\cdot t^{11}+\frac{8890091519570440470013334423795395721784966715729212467981251325429378022294140625}{2328144141574846005914060038668517841384150941696}\cdot t^9-\frac{176580526496200316084417499422523508489665223819475281897557244700590807145551921875}{74500612530395072189249921237392570924292830134272}\cdot t^7+\frac{122463203540870776731868272354616512674335354101420905795428808846992256027234109375}{149001225060790144378499842474785141848585660268544}\cdot t^5-\frac{38583638692680639631987824976547091793239227202576336739486211715983009372662734375}{298002450121580288756999684949570283697171320537088}\cdot t^3+\frac{3451477926405291624802425198377682914298993076555670896287536604504143207440078125}{596004900243160577513999369899140567394342641074176}\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.