Rule: Q[1, 20, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^{21}-\frac{210}{41}\cdot t^{19}+\frac{5985}{533}\cdot t^{17}-\frac{271320}{19721}\cdot t^{15}+\frac{203490}{19721}\cdot t^{13}-\frac{81396}{16687}\cdot t^{11}+\frac{67830}{47027}\cdot t^9-\frac{348840}{1363783}\cdot t^7+\frac{33915}{1363783}\cdot t^5-\frac{4522}{4091349}\cdot t^3+\frac{2261}{156835045}\cdot t$
• $P_3$:
  $t^{43}-\frac{19823}{1845}\cdot t^{41}+\frac{66431474}{1237275}\cdot t^{39}-\frac{1286508148622}{7764852375}\cdot t^{37}+\frac{2667193630954157}{7545547760625}\cdot t^{35}-\frac{109504976674009178093}{197957445499996875}\cdot t^{33}+\frac{38012393182426670482563752}{57815901436014314578125}\cdot t^{31}-\frac{28035935678183574928939058776}{46243396003418546127890625}\cdot t^{29}+\frac{1486043198956788735459651315386362}{3382696444650755715023108203125}\cdot t^{27}-\frac{114575214288433215563187381367411093054}{454989585287749897449183168861328125}\cdot t^{25}+\frac{134198371311099897378943373504210786530149716}{1173047323945097469355022308210743251953125}\cdot t^{23}-\frac{13472461789633675568271466371948256994616268}{327870370046766373422211204158282275390625}\cdot t^{21}+\frac{253377074314281655367196017988036963716782}{21858024669784424894814080277218818359375}\cdot t^{19}-\frac{39934028056166810561327273205833699014282}{15722438797564235450655741953788974609375}\cdot t^{17}+\frac{15335820185172600198007404932717412473864}{36069124300294422504445525658692353515625}\cdot t^{15}-\frac{1817688606456804286640369167457994151496}{34219425618228041863191908958246591796875}\cdot t^{13}+\frac{1191380666694345126935740808153099247251}{248575072887128228628846885828772412109375}\cdot t^{11}-\frac{214170983736513862382978877568264626689}{718607937982788879127030088123178427734375}\cdot t^9+\frac{85982544745612840840111490665998874}{7216341456905233318088089644256083984375}\cdot t^7-\frac{8435522716368226455139205955244040482}{30763263630787009635009526153463686025390625}\cdot t^5+\frac{2474222748712072630566579046552932907}{830608118031249260145257206143519522685546875}\cdot t^3-\frac{9556867509833570735257493967697541}{988819188132439595411020483504189907958984375}\cdot t$

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.