Rule: Q[3, 4, 42, 48]

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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^7-8\cdot t^5+\frac{19}{4}\cdot t^3-\frac{3}{4}\cdot t$
• $P_3$:
  $4\cdot t^{49}-50\cdot t^{47}+\frac{587}{2}\cdot t^{45}-\frac{4301}{4}\cdot t^{43}+\frac{88193}{32}\cdot t^{41}-\frac{336077}{64}\cdot t^{39}+\frac{1974765}{256}\cdot t^{37}-\frac{4578639}{512}\cdot t^{35}+\frac{34024497}{4096}\cdot t^{33}-\frac{51138329}{8192}\cdot t^{31}+\frac{125047087}{32768}\cdot t^{29}-\frac{124632865}{65536}\cdot t^{27}+\frac{404709123}{524288}\cdot t^{25}-\frac{266611935}{1048576}\cdot t^{23}+\frac{283171515}{4194304}\cdot t^{21}-\frac{120029985}{8388608}\cdot t^{19}+\frac{2563431075}{1073741824}\cdot t^{17}-\frac{660960315}{2147483648}\cdot t^{15}+\frac{256818345}{8589934592}\cdot t^{13}-\frac{36324015}{17179869184}\cdot t^{11}+\frac{14257815}{137438953472}\cdot t^9-\frac{904475}{274877906944}\cdot t^7+\frac{66355}{1099511627776}\cdot t^5-\frac{1153}{2199023255552}\cdot t^3+\frac{3}{2199023255552}\cdot t$
• $P_4$:
  $4\cdot t^{97}-98\cdot t^{95}+\frac{2327}{2}\cdot t^{93}-\frac{35673}{4}\cdot t^{91}+\frac{1587495}{32}\cdot t^{89}-\frac{13659987}{64}\cdot t^{87}+\frac{189226015}{256}\cdot t^{85}-\frac{1084095661}{512}\cdot t^{83}+\frac{41913454457}{8192}\cdot t^{81}-\frac{173397670065}{16384}\cdot t^{79}+\frac{1242147110139}{65536}\cdot t^{77}-\frac{3886353105453}{131072}\cdot t^{75}+\frac{42786936888345}{1048576}\cdot t^{73}-\frac{104188931770005}{2097152}\cdot t^{71}+\frac{450964689968925}{8388608}\cdot t^{69}-\frac{870563993088335}{16777216}\cdot t^{67}+\frac{12027514042842265}{268435456}\cdot t^{65}-\frac{18623855223295465}{536870912}\cdot t^{63}+\frac{51801351402172295}{2147483648}\cdot t^{61}-\frac{64781978114598425}{4294967296}\cdot t^{59}+\frac{291626475643681355}{34359738368}\cdot t^{57}-\frac{295451085160319799}{68719476736}\cdot t^{55}+\frac{538882312503118059}{274877906944}\cdot t^{53}-\frac{442179619213186881}{549755813888}\cdot t^{51}+\frac{2609524661195888475}{8796093022208}\cdot t^{49}-\frac{1728528720992220147}{17592186044416}\cdot t^{47}+\frac{2052896771738402121}{70368744177664}\cdot t^{45}-\frac{1090675709979525439}{140737488355328}\cdot t^{43}+\frac{2068628998024908319}{1125899906842624}\cdot t^{41}-\frac{872830290167596915}{2251799813685248}\cdot t^{39}+\frac{653159054437969443}{9007199254740992}\cdot t^{37}-\frac{215836176517939425}{18014398509481984}\cdot t^{35}+\frac{8024672374733464611}{4611686018427387904}\cdot t^{33}-\frac{2037571285131696979}{9223372036854775808}\cdot t^{31}+\frac{898734061140464885}{36893488147419103232}\cdot t^{29}-\frac{170869828261660283}{73786976294838206464}\cdot t^{27}+\frac{111041353445091069}{590295810358705651712}\cdot t^{25}-\frac{15256617295479105}{1180591620717411303424}\cdot t^{23}+\frac{3501895202770965}{4722366482869645213696}\cdot t^{21}-\frac{330741676378575}{9444732965739290427392}\cdot t^{19}+\frac{201944917746495}{151115727451828646838272}\cdot t^{17}-\frac{12176744551335}{302231454903657293676544}\cdot t^{15}+\frac{1127232040445}{1208925819614629174706176}\cdot t^{13}-\frac{38571760955}{2417851639229258349412352}\cdot t^{11}+\frac{3708019175}{19342813113834066795298816}\cdot t^9-\frac{58152395}{38685626227668133590597632}\cdot t^7+\frac{1061683}{154742504910672534362390528}\cdot t^5-\frac{4609}{309485009821345068724781056}\cdot t^3+\frac{3}{309485009821345068724781056}\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.