Rule: Q[26, 41]

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.

• $P_1$:
  $67108864\cdot t^{26}-10905190400\cdot t^{24}+752458137600\cdot t^{22}-28969638297600\cdot t^{20}+688028909568000\cdot t^{18}-10526842316390400\cdot t^{16}+105268423163904000\cdot t^{14}-684244750565376000\cdot t^{12}+2822509596082176000\cdot t^{10}-7056273990205440000\cdot t^8+9878783586287616000\cdot t^6-6735534263377920000\cdot t^4+1683883565844480000\cdot t^2-64764752532480000$
• $P_2$:
  $67108864\cdot t^{67}-\frac{18476417561722653006300122550835143914483230928291166101469921280}{347370223533358277498175832229340565547938809983077593}\cdot t^{65}+\frac{6859507468362932600585381700619019259375273462534281425160587182080}{347370223533358277498175832229340565547938809983077593}\cdot t^{63}-\frac{176394677421965834921341485504790895778862668420192557793229165035520}{38596691503706475277575092469926729505326534442564177}\cdot t^{61}+\frac{85722099753986342251202480729002108480605705535820270043629943468851200}{115790074511119425832725277409780188515979603327692531}\cdot t^{59}-\frac{10345185512861692754232767809483393773726510676317581604312547351278387200}{115790074511119425832725277409780188515979603327692531}\cdot t^{57}+\frac{322228804721976990925463196002944160895126521735430696577866258692282777600}{38596691503706475277575092469926729505326534442564177}\cdot t^{55}-\frac{7973820071377667400051915041362967676152262219984164604861002861511180288000}{12865563834568825092525030823308909835108844814188059}\cdot t^{53}+\frac{478825520891858610109835866824542204665657267148614160417523307067388198912000}{12865563834568825092525030823308909835108844814188059}\cdot t^{51}-\frac{23560179839658498076175655298997788291661297352677244780586238289790272405504000}{12865563834568825092525030823308909835108844814188059}\cdot t^{49}+\frac{958791277005067134221517759185149413334935886352197784601411337288790117528371200}{12865563834568825092525030823308909835108844814188059}\cdot t^{47}-\frac{32487705809863537555916106782503958996904349610793008280064129695058985406038016000}{12865563834568825092525030823308909835108844814188059}\cdot t^{45}+\frac{920819684842141998015355295857324431084696789128861230059487534080969464941092864000}{12865563834568825092525030823308909835108844814188059}\cdot t^{43}-\frac{21896391105342601214833920204174808713085565761372400028396983680089557860148465664000}{12865563834568825092525030823308909835108844814188059}\cdot t^{41}+\frac{437494645536770156010377044417098557491531387799608273375988930931064918122734407680000}{12865563834568825092525030823308909835108844814188059}\cdot t^{39}-\frac{7346502881383476875533389941567229896081452724469480197571853733285071705739026593792000}{12865563834568825092525030823308909835108844814188059}\cdot t^{37}+\frac{103582274030262304445353768456969997014621349190624789503118400755283879869038850881280000}{12865563834568825092525030823308909835108844814188059}\cdot t^{35}-\frac{1223698316835224358581195180278863149815468640330526427741349807789944445578687835982720000}{12865563834568825092525030823308909835108844814188059}\cdot t^{33}+\frac{12073302000514303930408873365028146524341265717894250847073608770613309571569311948702720000}{12865563834568825092525030823308909835108844814188059}\cdot t^{31}-\frac{99033716352416211340490526585820211633695395827516377219448911142408004783946603071609600000}{12865563834568825092525030823308909835108844814188059}\cdot t^{29}+\frac{671431319650044254347927364616495451510955166365375620816037571864597468885451949543883360000}{12865563834568825092525030823308909835108844814188059}\cdot t^{27}-\frac{3734858712103058663870392011252803597070276474939269001444947586318286399521177886068270000000}{12865563834568825092525030823308909835108844814188059}\cdot t^{25}+\frac{16889537266986187994836552272784064805920073235018478814407897932557827225013807391928274000000}{12865563834568825092525030823308909835108844814188059}\cdot t^{23}-\frac{61392392094874664419463763304311313547336559760280585008355018785269201616370387573489799000000}{12865563834568825092525030823308909835108844814188059}\cdot t^{21}+\frac{176882959299720794270256404195801080075110717306784216222111235627436182317978367322511635000000}{12865563834568825092525030823308909835108844814188059}\cdot t^{19}-\frac{396978130687114472479648735239863903873550002103505559991336704949825292419578338027118671500000}{12865563834568825092525030823308909835108844814188059}\cdot t^{17}+\frac{678926403410531940237153644047194727796097567339265523943253327053686766197725834589941443750000}{12865563834568825092525030823308909835108844814188059}\cdot t^{15}-\frac{860241794099574177677928429272273584890036970074071809039017763486321775622773553723657997500000}{12865563834568825092525030823308909835108844814188059}\cdot t^{13}+\frac{778164573536132374552512141843412059453748609660171541604783568389761230331133696035041111171875}{12865563834568825092525030823308909835108844814188059}\cdot t^{11}-\frac{955764581167530899554475954406683299986569964353773416071215848068190238006813736361116073046875}{25731127669137650185050061646617819670217689628376118}\cdot t^9+\frac{370965678493116523469322700326059937826511636239037631888187996157097874715722830116591613984375}{25731127669137650185050061646617819670217689628376118}\cdot t^7-\frac{163085286946746061196322263801433987443630793950360988859889800231135965963099669580679333203125}{51462255338275300370100123293235639340435379256752236}\cdot t^5+\frac{266855148052301404998026147698827551689093317914562088399632586549891165138766978628262196484375}{823396085412404805921601972691770229446966068108035776}\cdot t^3-\frac{15665842203543451257435272427605365494450235123019359800244599736175521790675037906326058984375}{1646792170824809611843203945383540458893932136216071552}\cdot t$

Warning: This rule has negative weights!

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.