Rule: Q[27, 44]

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.

• $P_1$:
  $134217728\cdot t^{27}-23555211264\cdot t^{25}+1766640844800\cdot t^{23}-74493355622400\cdot t^{21}+1955450585088000\cdot t^{19}-33438205005004800\cdot t^{17}+378966323390054400\cdot t^{15}-2842247425425408000\cdot t^{13}+13855956198948864000\cdot t^{11}-42337643941232640000\cdot t^9+76207759094218752000\cdot t^7-72743770044481536000\cdot t^5+30309904185200640000\cdot t^3-3497296636753920000\cdot t$
• $P_2$:
  $134217728\cdot t^{71}-\frac{276754539854449749528579672286242587842086354117958836571602944}{2240758616243123085684006629009389718779104141555315}\cdot t^{69}+\frac{1158106485420299352790806595501084187563281230291262142337555365888}{21660666623683523161612064080424100614864673368368045}\cdot t^{67}-\frac{313913790248838974299676453516921342296153659748163023588328982183936}{21660666623683523161612064080424100614864673368368045}\cdot t^{65}+\frac{107694705254817781488850836993596393276871675856248282076613038900772864}{38989199922630341690901715344763381106756412063062481}\cdot t^{63}-\frac{1707270152601698676949060330131219939293402860951749666551590252951109632}{4332133324736704632322412816084820122972934673673609}\cdot t^{61}+\frac{189550315267354330120471612167263786584975187714703288520663677684028538880}{4332133324736704632322412816084820122972934673673609}\cdot t^{59}-\frac{16807186815663940696736051879501791001263175627828642942857924335821630996480}{4332133324736704632322412816084820122972934673673609}\cdot t^{57}+\frac{1212110062616002505866385869928944099385620602214850698141105473155031084564480}{4332133324736704632322412816084820122972934673673609}\cdot t^{55}-\frac{72044827658874709767545892880866821430612208303634588989048887410435464966963200}{4332133324736704632322412816084820122972934673673609}\cdot t^{53}+\frac{3563578995546007556751347694015916810666613522481827792202662474327676456704409600}{4332133324736704632322412816084820122972934673673609}\cdot t^{51}-\frac{147733420840565502177820169851564064202683847011425779211894658441849266854781255680}{4332133324736704632322412816084820122972934673673609}\cdot t^{49}+\frac{5159427924680062856199436860253347033965635896561273662358679827842211283269813534720}{4332133324736704632322412816084820122972934673673609}\cdot t^{47}-\frac{152329035476858663384550599615369528592324908092620122326156816231826578741427833405440}{4332133324736704632322412816084820122972934673673609}\cdot t^{45}+\frac{3810397929328998821422729519031191485596961950687704414296056499256055323573689473433600}{4332133324736704632322412816084820122972934673673609}\cdot t^{43}-\frac{80836686519171004815715952016335939945493334995274391907324895847400538834111186064179200}{4332133324736704632322412816084820122972934673673609}\cdot t^{41}+\frac{16341624679212749120644983792598669187938526941695330740883191141482080633466967869747200}{48675655334120276767667559731290113741268928917681}\cdot t^{39}-\frac{22169687253208528914072105627413134388537150151425645214055376114356567464209643930430003200}{4332133324736704632322412816084820122972934673673609}\cdot t^{37}+\frac{285739973920583689467998188534221318278505389605866747407024460286607753987081825691056102400}{4332133324736704632322412816084820122972934673673609}\cdot t^{35}-\frac{3104796768030564796826892067219064367942465143523118777488291987284895846332415477561217728000}{4332133324736704632322412816084820122972934673673609}\cdot t^{33}+\frac{28327729377116227424583543520005112732924378243463119291643316484805586977823399362171663616000}{4332133324736704632322412816084820122972934673673609}\cdot t^{31}-\frac{7445387175065158739109981086103670658729913291540586245613211520484489210305580825614992256000}{149383907749541539045600441933959314585273609437021}\cdot t^{29}+\frac{47107263642264832574986814935276425955083395665710763276426723781612840519422713528026557824000}{149383907749541539045600441933959314585273609437021}\cdot t^{27}-\frac{245480446954914630291777069937718553657450610067071920891700544431641651125854590568891020288000}{149383907749541539045600441933959314585273609437021}\cdot t^{25}+\frac{1043583796256899461018817034503285892268936565234368740724250082717369950976577440940224136900000}{149383907749541539045600441933959314585273609437021}\cdot t^{23}-\frac{3577338849116658617988424041201330151371901432120030139385492372446615794655533769398872319050000}{149383907749541539045600441933959314585273609437021}\cdot t^{21}+\frac{9747970761439816096217619698021686738388597375455045072339720732649385816103821102319073652525000}{149383907749541539045600441933959314585273609437021}\cdot t^{19}-\frac{20745200878386462060239564073386225314902326576427237767077255099881565400746082998136510288662500}{149383907749541539045600441933959314585273609437021}\cdot t^{17}+\frac{33724201624463129229475221771787380454578575381731638366256298606654467403916310563491535775950000}{149383907749541539045600441933959314585273609437021}\cdot t^{15}-\frac{40705775590771446015565270287291166806269156411890064503694899382145700322950296052516212298500000}{149383907749541539045600441933959314585273609437021}\cdot t^{13}+\frac{35141185295234019041346227734046325431893539636787351778102385118814852386014239230213594904343750}{149383907749541539045600441933959314585273609437021}\cdot t^{11}-\frac{20611407803754581181689165976626587266370599852325481626243863844828232571235837407556253242828125}{149383907749541539045600441933959314585273609437021}\cdot t^9+\frac{243734256325537179260809527851432366121649351663547109413691906594921650236014583162728743806453125}{4780285047985329249459214141886698066728755501984672}\cdot t^7-\frac{100273154854445507169319688790360148108481168327445002320009670519331115914909285988167113044640625}{9560570095970658498918428283773396133457511003969344}\cdot t^5+\frac{201833253874725784362905665900184266125232413344988491373312343815555575094758059701198079453125}{214844271819565359526256815365694295133876651774592}\cdot t^3-\frac{698702956871074888834996210496515643563832302762889908059187431739722314206534208591870404453125}{38242280383882633995673713135093584533830044015877376}\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.