Rule: Q[4, 5, 34]

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^{43}-\frac{15336933931005901546930628393292801598850451598540242}{20059506747419960058056579667371585555506498480433}\cdot t^{41}+\frac{5288322184205571730035776815607944887300673535223579669}{20059506747419960058056579667371585555506498480433}\cdot t^{39}-\frac{1090539690082734719528360968027986247505558577706064927043}{20059506747419960058056579667371585555506498480433}\cdot t^{37}+\frac{150401439024545424137986941881490107856187814350504649784348}{20059506747419960058056579667371585555506498480433}\cdot t^{35}-\frac{14698447451988240151112010271496672452663613958671157767775465}{20059506747419960058056579667371585555506498480433}\cdot t^{33}+\frac{33947714381480272084134774593974033721822386593295554770881980}{647080862819998711550212247334567275984080596143}\cdot t^{31}-\frac{1816163335923050490492322512605538884933771746859528322193552980}{647080862819998711550212247334567275984080596143}\cdot t^{29}+\frac{73405088528756954908774759925065914053688138795690822173741372610}{647080862819998711550212247334567275984080596143}\cdot t^{27}-\frac{2252087408031867798434939929856842226574490065555517359092929852560}{647080862819998711550212247334567275984080596143}\cdot t^{25}+\frac{52432548646092829980350916814410559814343557353617812076832573916250}{647080862819998711550212247334567275984080596143}\cdot t^{23}-\frac{921884982952121230146186761024921001495285151650187884741997197279750}{647080862819998711550212247334567275984080596143}\cdot t^{21}+\frac{12127319138315958201755300550208197877221274364513501543095841022025500}{647080862819998711550212247334567275984080596143}\cdot t^{19}-\frac{117677543945744959072766855130084602500930303415291930352326846281502250}{647080862819998711550212247334567275984080596143}\cdot t^{17}+\frac{825634267939774074667544545898927197310801821751309336820444106416163500}{647080862819998711550212247334567275984080596143}\cdot t^{15}-\frac{4075798567908040710036875572803744280183121033863709028308406437132722500}{647080862819998711550212247334567275984080596143}\cdot t^{13}+\frac{13642969518169130880219279309759024292472915833167002849463155758984434375}{647080862819998711550212247334567275984080596143}\cdot t^{11}-\frac{29434729669306302138280399314876539095552745095738485734234416766432216250}{647080862819998711550212247334567275984080596143}\cdot t^9+\frac{38123286340579468912421916378365224863238683289983072327241009523025541875}{647080862819998711550212247334567275984080596143}\cdot t^7-\frac{26716644994983363570748602427077799763813671295959198742986804091838373125}{647080862819998711550212247334567275984080596143}\cdot t^5+\frac{8565801792379856340719646398923711604014819892919715615860082503613725000}{647080862819998711550212247334567275984080596143}\cdot t^3-\frac{863817637993491677133618565073031744825507495853918668437442550713534375}{647080862819998711550212247334567275984080596143}\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.