Rule: Q[22, 37]

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.

• $P_1$:
  $t^{22}-231\cdot t^{20}+21945\cdot t^{18}-1119195\cdot t^{16}+33575850\cdot t^{14}-611080470\cdot t^{12}+6721885170\cdot t^{10}-43212118950\cdot t^8+151242416325\cdot t^6-252070693875\cdot t^4+151242416325\cdot t^2-13749310575$
• $P_2$:
  $t^{59}-\frac{133192556749715850898883777857029}{104779331696056756994688859075}\cdot t^{57}+\frac{157323832934608034350646554715242383}{209558663392113513989377718150}\cdot t^{55}-\frac{264111886199418518480894574436934368587}{963969851603722164351137503490}\cdot t^{53}+\frac{66830782682385618075431914842392027308911}{963969851603722164351137503490}\cdot t^{51}-\frac{2494209711153774364606878857227170976738617}{192793970320744432870227500698}\cdot t^{49}+\frac{891079500337080116739726319460390516924327643}{481984925801861082175568751745}\cdot t^{47}-\frac{99963685163894018699863244238031808662894756893}{481984925801861082175568751745}\cdot t^{45}+\frac{1790730784669334666851538905292453312286285830508}{96396985160372216435113750349}\cdot t^{43}-\frac{129568887993398582661998524940391024661179283722456}{96396985160372216435113750349}\cdot t^{41}+\frac{1174437386309121179569434644853411823687117587015975}{14830305409288033297709807746}\cdot t^{39}-\frac{56633330300219498697244053146813430951415046528567769}{14830305409288033297709807746}\cdot t^{37}+\frac{2241550270288475803770382435488331961355454418053547169}{14830305409288033297709807746}\cdot t^{35}-\frac{72886253958062268754636093906957951141290364336743765555}{14830305409288033297709807746}\cdot t^{33}+\frac{972645481132569009868964555011667837713087488092649601650}{7415152704644016648854903873}\cdot t^{31}-\frac{21253255899743030066008766138875231197037577363765194425150}{7415152704644016648854903873}\cdot t^{29}+\frac{378601358471919279486959819014505631805020352399020927122925}{7415152704644016648854903873}\cdot t^{27}-\frac{5465096136462088702948066851697261721194748243128057819829475}{7415152704644016648854903873}\cdot t^{25}+\frac{126825778927931783688695781570307444202263812034172581707487875}{14830305409288033297709807746}\cdot t^{23}-\frac{50900314259127202795262127614992297993170947478053514107914875}{644795887360349273813469902}\cdot t^{21}+\frac{368892058897060237176233710796037757693458204724678804789044375}{644795887360349273813469902}\cdot t^{19}-\frac{2064232006794952016469249466129428640028999622463207992397711125}{644795887360349273813469902}\cdot t^{17}+\frac{4365178114891828375976909398129475327882323198305898034429827125}{322397943680174636906734951}\cdot t^{15}-\frac{13573226541764359512112877067644374622643025796184740306915821875}{322397943680174636906734951}\cdot t^{13}+\frac{29911914200461134873040614993160480513368215763863574827281526250}{322397943680174636906734951}\cdot t^{11}-\frac{44423813864699791233190060700988796981266212161860680373873731250}{322397943680174636906734951}\cdot t^9+\frac{82690123261719371557722400654468672889829855720797022720678384375}{644795887360349273813469902}\cdot t^7-\frac{43059770877605033865122550893866932647923414272348478771780115625}{644795887360349273813469902}\cdot t^5+\frac{10260314917027782078966752663381082515573578632233123841373265625}{644795887360349273813469902}\cdot t^3-\frac{704503478680034222476782987315170565972480441964681437177046875}{644795887360349273813469902}\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.