Rule: Q[1, 24, 42]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{25}-300\cdot t^{23}+18975\cdot t^{21}-664125\cdot t^{19}+\frac{113565375}{8}\cdot t^{17}-\frac{386122275}{2}\cdot t^{15}+\frac{13514279625}{8}\cdot t^{13}-\frac{75293843625}{8}\cdot t^{11}+\frac{4141161399375}{128}\cdot t^9-\frac{4141161399375}{64}\cdot t^7+\frac{17392877877375}{256}\cdot t^5-\frac{7905853580625}{256}\cdot t^3+\frac{7905853580625}{2048}\cdot t$
• $P_3$:
  $2\cdot t^{67}-\frac{5916977598948764630874254250821757333879879437}{3561065251525204731467607869168469441659291}\cdot t^{65}+\frac{4609577178572112675164169785529174318046805706755}{7122130503050409462935215738336938883318582}\cdot t^{63}-\frac{20165505037782828327421163541792781460837712778625635}{128198349054907370332833883290064899899734476}\cdot t^{61}+\frac{762914850404979908321930370643142727825827031740377475}{28488522012201637851740862953347755533274328}\cdot t^{59}-\frac{7553124481990293657380705644203097694138279895318879387725}{2222104716951727752435787310361124931595397584}\cdot t^{57}+\frac{1485565111913984004262376522691561755050020889984215671905025}{4444209433903455504871574620722249863190795168}\cdot t^{55}-\frac{242691617359830665824388529918556880470048973057662245500125}{9287794010247555914047177890746603684829248}\cdot t^{53}+\frac{890437278134685778303352613022571195383817782261929347753848125}{538692052594358243014736317663303013720096384}\cdot t^{51}-\frac{92338847343136373161922828674633238601424478041113781156298596125}{1077384105188716486029472635326606027440192768}\cdot t^{49}+\frac{7921380141313499136619668514409355189144123508312422131902832873025}{2154768210377432972058945270653212054880385536}\cdot t^{47}-\frac{565859652374422825062878634481027077764748096541010793929554367986425}{4309536420754865944117890541306424109760771072}\cdot t^{45}+\frac{33811986210186187251733723751983327514974906029312899056325434443146625}{8619072841509731888235781082612848219521542144}\cdot t^{43}-\frac{1694812173354746539189636999577503548785755432304135645303175745531133625}{17238145683019463776471562165225696439043084288}\cdot t^{41}+\frac{71363567425158628525575547776689662266960422527512510274240457311800598125}{34476291366038927552943124330451392878086168576}\cdot t^{39}-\frac{194202979815928171075793753986761298672573772385168422728651935448760891625}{5304044825544450392760480666223291212013256704}\cdot t^{37}+\frac{5766296974659758959962876941986006351929462874865528969294555218342248786375}{10608089651088900785520961332446582424026513408}\cdot t^{35}-\frac{143386774750226855522789038217513830244770459176946547812911557823375456991875}{21216179302177801571041922664893164848053026816}\cdot t^{33}+\frac{2976048939881581680855755384078951008888197508126919699771895696116370631156875}{42432358604355603142083845329786329696106053632}\cdot t^{31}-\frac{1769733150885885360690283562648661688399640100537061546970219251493313509259375}{2926369558921076078764403126192160668696969216}\cdot t^{29}+\frac{25208199096145729176812242216548250112920116104718446415589653939244582256874375}{5852739117842152157528806252384321337393938432}\cdot t^{27}-\frac{294386605193553445122507259540438205216561718731853649506219286176689266158039375}{11705478235684304315057612504768642674787876864}\cdot t^{25}+\frac{2792791062320166676239932195922297215019149152130086666869115081909149103781296875}{23410956471368608630115225009537285349575753728}\cdot t^{23}-\frac{21280106714680014373273116995380901838971276609393458237190158539648345365062171875}{46821912942737217260230450019074570699151507456}\cdot t^{21}+\frac{128421352610596332435520742356272730359276491496797648007120846658954151973607734375}{93643825885474434520460900038149141398303014912}\cdot t^{19}-\frac{603194969321853211257048301214608136674672772374758969431305874088639458118780984375}{187287651770948869040921800076298282796606029824}\cdot t^{17}+\frac{2157233866044564080552871563803156653514967036549387851230248611317937726921851421875}{374575303541897738081843600152596565593212059648}\cdot t^{15}-\frac{5710996387010066861469398700313793645430087180113885704097798894390580548448558046875}{749150607083795476163687200305193131186424119296}\cdot t^{13}+\frac{10783732993347405034067943950100278051064517361187711904757781310932715993177587421875}{1498301214167590952327374400610386262372848238592}\cdot t^{11}-\frac{13805375320203379911673828899015564949233851222027401063406799518495004867522723046875}{2996602428335181904654748801220772524745696477184}\cdot t^9+\frac{11143441182238159112628191422387377054583455811163262609478441875046875134717336484375}{5993204856670363809309497602441545049491392954368}\cdot t^7-\frac{5074614049429138422357103796259820194270549477383562976453089088428668095884073359375}{11986409713340727618618995204883090098982785908736}\cdot t^5+\frac{269555714279732911561688563562658819540256974465123876729223486903148928761152734375}{5993204856670363809309497602441545049491392954368}\cdot t^3-\frac{35188799793056631270925236729354114050963505844521157257023490879880514774609765625}{23972819426681455237237990409766180197965571817472}\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.