Rule: Q[21, 22]

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.

• $P_1$:
  $\frac{67282234305}{262144}\cdot t^{21}-\frac{172308161025}{131072}\cdot t^{19}+\frac{755505013725}{262144}\cdot t^{17}-\frac{115707975075}{32768}\cdot t^{15}+\frac{347123925225}{131072}\cdot t^{13}-\frac{82047473235}{65536}\cdot t^{11}+\frac{48522699225}{131072}\cdot t^9-\frac{2151252675}{32768}\cdot t^7+\frac{1673196525}{262144}\cdot t^5-\frac{37182145}{131072}\cdot t^3+\frac{969969}{262144}\cdot t$
• $P_2$:
  $\frac{67282234305}{262144}\cdot t^{43}-\frac{2168675984761}{786432}\cdot t^{41}+\frac{11460661535626963}{831651840}\cdot t^{39}-\frac{77981209631420871061}{1833792307200}\cdot t^{37}+\frac{11963649787644086132517059}{131868004810752000}\cdot t^{35}-\frac{44652966655419667419234539881}{314505191473643520000}\cdot t^{33}+\frac{687515791557477379540021983646213}{4074218189796380774400000}\cdot t^{31}-\frac{542046090017085162405575137250861641}{3483456552275905562112000000}\cdot t^{29}+\frac{3332810223318746375652697389180888656184947}{29558452559550923538633922560000000}\cdot t^{27}-\frac{256962547109998248695564864192718148470512867249}{3975759661522396970563955753932800000000}\cdot t^{25}+\frac{6542874102828125610660524224230028292340486332348701}{222831389629176544207683310118548608000000000}\cdot t^{23}-\frac{15107622179921542995046580404722515107468781119011229}{1432487504758992069906535565047812480000000000}\cdot t^{21}+\frac{568259189384296518139298109771136589326443672820217}{190998333967865609320871408673041664000000000}\cdot t^{19}-\frac{2184431408469478901099000136277765390198186231987}{3350847964348519461769673836369152000000000}\cdot t^{17}+\frac{16132399108163404837217379812509470081611121587}{147831527838905270372191492780992000000000}\cdot t^{15}-\frac{671820208268268742448174574800079893134879907}{49277175946301756790730497593664000000000}\cdot t^{13}+\frac{320244314588106664465454064972361230760316051}{260332250282348903800085647664640000000000}\cdot t^{11}-\frac{633263120592945289946478157961498099104928779}{8278565558978695140842723595735552000000000}\cdot t^9+\frac{4100550550190649186085337045606819300497}{1340875535953789300428040750848000000000}\cdot t^7-\frac{13872217107067548405476424193398824572649}{197108703785207027162921990374656000000000}\cdot t^5+\frac{8137718620514006881933478484112596331123}{10643870004401179466797787480231424000000000}\cdot t^3-\frac{31432537239842614148261897659757212349}{12671273814763308889044985095513600000000000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.