Rule: Q[23, 40]

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.

• $P_1$:
  $8388608\cdot t^{23}-1061158912\cdot t^{21}+55710842880\cdot t^{19}-1587759022080\cdot t^{17}+26991903375360\cdot t^{15}-283414985441280\cdot t^{13}+1842197405368320\cdot t^{11}-7237204092518400\cdot t^9+16283709208166400\cdot t^7-18997660742860800\cdot t^5+9498830371430400\cdot t^3-1295295050649600\cdot t$
• $P_2$:
  $8388608\cdot t^{63}-\frac{426041370192985570006461204387722007362404352}{68193586028690041510290950788710897}\cdot t^{61}+\frac{4001949969584057058228982858282589809317012045824}{1841226822774631120777855671295194219}\cdot t^{59}-\frac{11248706023987481403072713171116669832298448219537408}{23935948696070204570112123726837524847}\cdot t^{57}+\frac{14137635432146116292384811954374796278901800799398526976}{199466239133918371417601031056979373725}\cdot t^{55}-\frac{1582463621180308896572492738362181480580192816398593163264}{199466239133918371417601031056979373725}\cdot t^{53}+\frac{27312899895141161938583564122235847854025251061487008874496}{39893247826783674283520206211395874745}\cdot t^{51}-\frac{621228041432583040017732979766034167421686690182062884061184}{13297749275594558094506735403798624915}\cdot t^{49}+\frac{757892850877895191414570426641840519653591584228146651430912}{295505539457656846544594120084413887}\cdot t^{47}-\frac{508346644060810806830383484947143620203952484926774511732604928}{4432583091864852698168911801266208305}\cdot t^{45}+\frac{691662586079905743239650064192274430824144833136777200778715136}{164169744143142692524774511158007715}\cdot t^{43}-\frac{37797522437808915411265581484782218415349681517715931005891596288}{295505539457656846544594120084413887}\cdot t^{41}+\frac{951884861522341374593089841016517899907959354066603513304376006656}{295505539457656846544594120084413887}\cdot t^{39}-\frac{510875227903135851768260665560412812353324148568072906291217093632}{7577065114298893501143438976523433}\cdot t^{37}+\frac{8891096216632471472603926969363960020233784806369851989944431988224}{7577065114298893501143438976523433}\cdot t^{35}-\frac{128526001396089597977691936441809999138867697657929322633970566454016}{7577065114298893501143438976523433}\cdot t^{33}+\frac{513158692623611555832134175530481421480765173512018514369505635095680}{2525688371432964500381146325507811}\cdot t^{31}-\frac{563746293785684818600293910725881856270139709411031685501089979227200}{280632041270329388931238480611979}\cdot t^{29}+\frac{13730277068169078172955238469669451141852179119169642565596297713800480}{841896123810988166793715441835937}\cdot t^{27}-\frac{30299470804942978325873455410653394420698662370020910133387847102806000}{280632041270329388931238480611979}\cdot t^{25}+\frac{162147448871432492828730410039292417874079078569180427795332769607966600}{280632041270329388931238480611979}\cdot t^{23}-\frac{693775788811897915125038732903305508642161159330208634364391005148734500}{280632041270329388931238480611979}\cdot t^{21}+\frac{2341086861578570631230446236178928012084052689598052643141943801819651750}{280632041270329388931238480611979}\cdot t^{19}-\frac{6124323394678754124607400231337404265109120953816716349369186448913322375}{280632041270329388931238480611979}\cdot t^{17}+\frac{24307580658897131636795402970939372502316826605495970620429045692800184125}{561264082540658777862476961223958}\cdot t^{15}-\frac{71168844974628612351311108469936831385423971620235521036118637908590116125}{1122528165081317555724953922447916}\cdot t^{13}+\frac{148131162606660819867922704156823534123270007645899012785803446311995784375}{2245056330162635111449907844895832}\cdot t^{11}-\frac{208354537352068978708205876973364687655820538235457879348067394202966241875}{4490112660325270222899815689791664}\cdot t^9+\frac{184055051774275561779045286426490164682047939389850504611743521998202288125}{8980225320650540445799631379583328}\cdot t^7-\frac{91034982005097905145522440858992727834030191379812125195035188321904053125}{17960450641301080891599262759166656}\cdot t^5+\frac{20520763577746853237416445346092614787121339481541213449796871073329984375}{35920901282602161783198525518333312}\cdot t^3-\frac{1307886506810393190133249938351352539627413446813812509274544609814596875}{71841802565204323566397051036666624}\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.