Rule: Q[4, 5, 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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{49}-\frac{71075838758475589337559527696671221462824647610569763781076808010759}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{47}+\frac{35247230006863756269303360180105555164777386797866930355898219625617902}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{45}-\frac{10641544608716326712093744772648720876570895521771557096204907223997452635}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{43}+\frac{2190866337377804835732821457129749276782195289549583405267133083356091326670}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{41}-\frac{326512641058774678259835041767286700987777437693488097786365172353724125384605}{65703617067213487295636604494416823944702401140119109814307960999}\cdot t^{39}+\frac{986455858180640001211166212296136165698925868426257957805869373958292445180790}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{37}-\frac{84571802597664457643962603268802089329563182035713047649233017831823366460174645}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{35}+\frac{5639455172878922191512496550325821538147144392540386318809662753952919961556355425}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{33}-\frac{294943635936417696802308089092136017849249217748031114390037401407862762914145768350}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{31}+\frac{12147651232343058851622036792279475791979563159605851785519942380902768742389132161900}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{29}-\frac{394203001134564340952109804232310811794072129194412324733103995975782058348400492902150}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{27}+\frac{10052276192484055173629073722048687365752938224974270908200040996691007150112551288205700}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{25}-\frac{200274056715629096605807404781028604339096162929550105510098720364128801602690321546901250}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{23}+\frac{3089512741831937538661386925975025301544728197572655667138691497237657008853700209857377500}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{21}-\frac{36439187947168567047143567843330132517499565274643516761412655346562229440181044666438016250}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{19}+\frac{323065995819006626062791227920677318873709028774490873010087976167189141875662334018667888125}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{17}-\frac{2105440655924597911646331306369769824762021121286630299508007141526541990330428303860392964375}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{15}+\frac{9793722206984152108328013751346287658116920001355126659001790465919098523193362879257495018750}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{13}-\frac{31272534244881653502844728613574178673583694603509767212330012670958568597362697986331281896875}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^{11}+\frac{65032694951319457055434086802604005012588052998006674149013943672552732980768121327097278743750}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^9-\frac{81876859482016365071696571275437591729408488303762422869781462253045911862077872937481706603125}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^7+\frac{56126866699250871949615392205653151532746189731325180017141704823500636044789851519333849168750}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^5-\frac{17629554654081322429842161044166187705560806342082522980550821946313475900017682675662359390625}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t^3+\frac{1720857074793974401419103100413461467137947217272018577471470745435319462667255339252903234375}{1775773434249013170152340662011265512018983814597813778765080027}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.