Rule: Q[3, 18, 22, 42]

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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{21}-21\cdot t^{19}+\frac{189}{4}\cdot t^{17}-\frac{119}{2}\cdot t^{15}+\frac{735}{16}\cdot t^{13}-\frac{5733}{256}\cdot t^{11}+\frac{7007}{1024}\cdot t^9-\frac{1287}{1024}\cdot t^7+\frac{2079}{16384}\cdot t^5-\frac{385}{65536}\cdot t^3+\frac{21}{262144}\cdot t$
• $P_3$:
  $4\cdot t^{43}-44\cdot t^{41}+\frac{901}{4}\cdot t^{39}-\frac{1425}{2}\cdot t^{37}+\frac{99789}{64}\cdot t^{35}-\frac{160293}{64}\cdot t^{33}+\frac{391391}{128}\cdot t^{31}-\frac{5797}{2}\cdot t^{29}+\frac{8850655}{4096}\cdot t^{27}-\frac{5224089}{4096}\cdot t^{25}+\frac{156547365}{262144}\cdot t^{23}-\frac{29004495}{131072}\cdot t^{21}+\frac{270405135}{4194304}\cdot t^{19}-\frac{61256475}{4194304}\cdot t^{17}+\frac{42456735}{16777216}\cdot t^{15}-\frac{1374365}{4194304}\cdot t^{13}+\frac{32947615}{1073741824}\cdot t^{11}-\frac{2129501}{1073741824}\cdot t^9+\frac{1418065}{17179869184}\cdot t^7-\frac{17017}{8589934592}\cdot t^5+\frac{6181}{274877906944}\cdot t^3-\frac{21}{274877906944}\cdot t$
• $P_4$:
  $4\cdot t^{85}-86\cdot t^{83}+892\cdot t^{81}-5945\cdot t^{79}+\frac{1831141}{64}\cdot t^{77}-\frac{13560547}{128}\cdot t^{75}+\frac{80384535}{256}\cdot t^{73}-\frac{391820565}{512}\cdot t^{71}+\frac{25615811325}{16384}\cdot t^{69}-\frac{89004181207}{32768}\cdot t^{67}+\frac{132927690929}{32768}\cdot t^{65}-\frac{86056018529}{16384}\cdot t^{63}+\frac{3111484832911}{524288}\cdot t^{61}-\frac{6167298918865}{1048576}\cdot t^{59}+\frac{10764573301519}{2097152}\cdot t^{57}-\frac{16594616082417}{4194304}\cdot t^{55}+\frac{724590381004479}{268435456}\cdot t^{53}-\frac{876386828841381}{536870912}\cdot t^{51}+\frac{117537743465025}{134217728}\cdot t^{49}-\frac{447564281106705}{1073741824}\cdot t^{47}+\frac{48368073978063525}{274877906944}\cdot t^{45}-\frac{36183601418599635}{549755813888}\cdot t^{43}+\frac{23947643403612915}{1099511627776}\cdot t^{41}-\frac{13992539490017025}{2199023255552}\cdot t^{39}+\frac{115172762172777855}{70368744177664}\cdot t^{37}-\frac{51988764864122541}{140737488355328}\cdot t^{35}+\frac{10253511006056829}{140737488355328}\cdot t^{33}-\frac{1758390578322763}{140737488355328}\cdot t^{31}+\frac{8341028974105135}{4503599627370496}\cdot t^{29}-\frac{2122571584427329}{9007199254740992}\cdot t^{27}+\frac{459760634073923}{18014398509481984}\cdot t^{25}-\frac{83925275384405}{36028797018963968}\cdot t^{23}+\frac{816426728002655}{4611686018427387904}\cdot t^{21}-\frac{101842634229525}{9223372036854775808}\cdot t^{19}+\frac{2560318641699}{4611686018427387904}\cdot t^{17}-\frac{405953191227}{18446744073709551616}\cdot t^{15}+\frac{789130130801}{1180591620717411303424}\cdot t^{13}-\frac{35385125399}{2361183241434822606848}\cdot t^{11}+\frac{1113061235}{4722366482869645213696}\cdot t^9-\frac{22825561}{9444732965739290427392}\cdot t^7+\frac{4356373}{302231454903657293676544}\cdot t^5-\frac{24703}{604462909807314587353088}\cdot t^3+\frac{21}{604462909807314587353088}\cdot t$

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.