Rule: Q[1, 100]

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^{101}-5050\cdot t^{99}+\frac{12248775}{2}\cdot t^{97}-4752524700\cdot t^{95}+\frac{5305005696375}{2}\cdot t^{93}-\frac{2269481436909225}{2}\cdot t^{91}+\frac{3097842161381092125}{8}\cdot t^{89}-\frac{433255353713155598625}{4}\cdot t^{87}+\frac{1620808278240915094456125}{64}\cdot t^{85}-\frac{321460308517781493733798125}{64}\cdot t^{83}+\frac{218785885977202084635223003875}{256}\cdot t^{81}-\frac{8055298529160622207024119688125}{64}\cdot t^{79}+\frac{8272791589447959006613770919704375}{512}\cdot t^{77}-\frac{931007238104797232821226681194423125}{512}\cdot t^{75}+\frac{369077869391544617296986291473503453125}{2048}\cdot t^{73}-\frac{16165610679349654237607999566539451246875}{1024}\cdot t^{71}+\frac{40171542538183890780455878922850536348484375}{32768}\cdot t^{69}-\frac{2771836435134688463851455645676687008045421875}{32768}\cdot t^{67}+\frac{680947817564755132619507603621239441643158640625}{131072}\cdot t^{65}-\frac{2329558323247846506329894433441082300358174296875}{8192}\cdot t^{63}+\frac{909925481060608845372456765702086746519902880359375}{65536}\cdot t^{61}-\frac{39646753103355099691228473362733779669795768358515625}{65536}\cdot t^{59}+\frac{6166872232712779597426537993057954274092778151038203125}{262144}\cdot t^{57}-\frac{106981826993582567798834289531744511102739934011488828125}{131072}\cdot t^{55}+\frac{52956004361823371060422973318213532995856267335686969921875}{2097152}\cdot t^{53}-\frac{1459467480211852106425257144649964969365798727771532891046875}{2097152}\cdot t^{51}+\frac{143140079790008571976323296879131179687799490608361879698828125}{8388608}\cdot t^{49}-\frac{779318212190046669648871283008603089411352782201081345026953125}{2097152}\cdot t^{47}+\frac{120348998196777207127204265276042848521953193937052704853448046875}{16777216}\cdot t^{45}-\frac{2054232900255335087171245217642800345460925206856589272498509765625}{16777216}\cdot t^{43}+\frac{123664820595371172247708962102096580796747697452766674204410287890625}{67108864}\cdot t^{41}-\frac{817783491033906139057430233255799969784944450897328006835616419921875}{33554432}\cdot t^{39}+\frac{605977566856124449041555802842547777610643838114920053065191767162109375}{2147483648}\cdot t^{37}-\frac{6114864538275437622146608555956618483161951457341465990021480559544921875}{2147483648}\cdot t^{35}+\frac{214020258839640316775131299458481646910668301006951309650751819584072265625}{8589934592}\cdot t^{33}-\frac{201790529763089441530838082346568409944344398092268377670708858464982421875}{1073741824}\cdot t^{31}+\frac{10425844037759621145759967587906034513791127234767199512986624354024091796875}{8589934592}\cdot t^{29}-\frac{57201252423383867367277660009322297467556725098857878409088776861267314453125}{8589934592}\cdot t^{27}+\frac{1056717873716196707679708350698532969005916342615742911662640035700254072265625}{34359738368}\cdot t^{25}-\frac{2032149757146532130153285289804871094242146812722582522428153914808180908203125}{17179869184}\cdot t^{23}+\frac{102826777711614525785756235664126477368652628723762675634864588089293953955078125}{274877906944}\cdot t^{21}-\frac{263336869749256712378156213286177563992890878438904413211238579253069882080078125}{274877906944}\cdot t^{19}+\frac{2144314510815376086507843451044588735370682867288221650434371288203569039794921875}{1099511627776}\cdot t^{17}-\frac{847752248461892871410077643436232755844223459160459722264751439522341248291015625}{274877906944}\cdot t^{15}+\frac{8092180553499886499823468414618585396694860291986206439799900104531439188232421875}{2199023255552}\cdot t^{13}-\frac{7013223146366568299847005959336107343802212253054712247826580090593913963134765625}{2199023255552}\cdot t^{11}+\frac{16770751002180924195286318598412430604744420605130833636107039347072402955322265625}{8796093022208}\cdot t^9-\frac{3211420404672942931012273774164082456227655009493138355850284130290460140380859375}{4398046511104}\cdot t^7+\frac{22479942832710600517085916419148577193593585066451968490951988912033220982666015625}{140737488355328}\cdot t^5-\frac{2293871717623530665008766981545773183019753578209384539893060093064614385986328125}{140737488355328}\cdot t^3+\frac{275264606114823679801052037785492781962370429385126144787167211167753726318359375}{562949953421312}\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.