Rule: Q[41, 82]

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.

• $P_1$:
  $1099511627776\cdot t^{41}-11269994184704\cdot t^{39}+53532472377344\cdot t^{37}-156371169312768\cdot t^{35}+314327181557760\cdot t^{33}-461013199618048\cdot t^{31}+510407471005696\cdot t^{29}-435347548798976\cdot t^{27}+289407177326592\cdot t^{25}-150732904857600\cdot t^{23}+61508749885440\cdot t^{21}-19570965872640\cdot t^{19}+4808383856640\cdot t^{17}-898269511680\cdot t^{15}+124759654400\cdot t^{13}-12475965440\cdot t^{11}+857722624\cdot t^9-37840704\cdot t^7+959728\cdot t^5-11480\cdot t^3+41\cdot t$
• $P_2$:
  $1099511627776\cdot t^{123}-33809982554112\cdot t^{121}+507149738311680\cdot t^{119}-4945414323175424\cdot t^{117}+35251661341458432\cdot t^{115}-195825966180728832\cdot t^{113}+882611619652173824\cdot t^{111}-3317945774616084480\cdot t^{109}+10613820015972974592\cdot t^{107}-29332832997360009216\cdot t^{105}+70866047860878606336\cdot t^{103}-151079281417692905472\cdot t^{101}+286392781966722662400\cdot t^{99}-485766218643556515840\cdot t^{97}+741064060945084907520\cdot t^{95}-1021250318555495096320\cdot t^{93}+1275966373475586455040\cdot t^{91}-1449800859984052867200\cdot t^{89}+1501963007327394451840\cdot t^{87}-1421772168626463219720\cdot t^{85}+1231972485921474197670\cdot t^{83}-\frac{1957237334075992854655}{2}\cdot t^{81}+713484356706370032525\cdot t^{79}-\frac{3823035309586654035147}{8}\cdot t^{77}+\frac{18831988747223147654613}{64}\cdot t^{75}-\frac{42660219406974885503307}{256}\cdot t^{73}+\frac{22226617089914750020359}{256}\cdot t^{71}-\frac{681890660104174738278915}{16384}\cdot t^{69}+\frac{1202793600454431530828823}{65536}\cdot t^{67}-\frac{1951120066474503385665831}{262144}\cdot t^{65}+\frac{90912404531070050228157}{32768}\cdot t^{63}-\frac{249020934150322311494517}{262144}\cdot t^{61}+\frac{2503891810412581483708605}{8388608}\cdot t^{59}-\frac{2884955479876045063047423}{33554432}\cdot t^{57}+\frac{760804518486808975648329}{33554432}\cdot t^{55}-\frac{2934531714163406048929269}{536870912}\cdot t^{53}+\frac{2582237996243405833604427}{2147483648}\cdot t^{51}-\frac{2069361059214545844026175}{8589934592}\cdot t^{49}+\frac{188356703222624296638915}{4294967296}\cdot t^{47}-\frac{248612449552694584452585}{34359738368}\cdot t^{45}+\frac{296537741032732094708505}{274877906944}\cdot t^{43}-\frac{159294217818296895610815}{1099511627776}\cdot t^{41}+\frac{19197715845238602939575}{1099511627776}\cdot t^{39}-\frac{66165150889868859433605}{35184372088832}\cdot t^{37}+\frac{25354424909466432901485}{140737488355328}\cdot t^{35}-\frac{8595944627425941638965}{562949953421312}\cdot t^{33}+\frac{160172881256384005695}{140737488355328}\cdot t^{31}-\frac{83404691807635568475}{1125899906842624}\cdot t^{29}+\frac{75249566386444535113}{18014398509481984}\cdot t^{27}-\frac{14568448870183139451}{72057594037927936}\cdot t^{25}+\frac{598703378226704361}{72057594037927936}\cdot t^{23}-\frac{330004258586832687}{1152921504606846976}\cdot t^{21}+\frac{37541112840322245}{4611686018427387904}\cdot t^{19}-\frac{3460663232180649}{18446744073709551616}\cdot t^{17}+\frac{31578784190591}{9223372036854775808}\cdot t^{15}-\frac{3546280577553}{73786976294838206464}\cdot t^{13}+\frac{294893267643}{590295810358705651712}\cdot t^{11}-\frac{8622610165}{2361183241434822606848}\cdot t^9+\frac{41168961}{2361183241434822606848}\cdot t^7-\frac{14653359}{302231454903657293676544}\cdot t^5+\frac{77531}{1208925819614629174706176}\cdot t^3-\frac{123}{4835703278458516698824704}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.