Rule: Q[14, 15, 84]

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.

• $P_1$:
  $8192\cdot t^{14}-28672\cdot t^{12}+39424\cdot t^{10}-26880\cdot t^8+9408\cdot t^6-1568\cdot t^4+98\cdot t^2-1$
• $P_2$:
  $8192\cdot t^{29}-61440\cdot t^{27}+206848\cdot t^{25}-412672\cdot t^{23}+542432\cdot t^{21}-494032\cdot t^{19}+319200\cdot t^{17}-147288\cdot t^{15}+\frac{192831}{4}\cdot t^{13}-\frac{87737}{8}\cdot t^{11}+\frac{26741}{16}\cdot t^9-\frac{5135}{32}\cdot t^7+\frac{17927}{2048}\cdot t^5-\frac{917}{4096}\cdot t^3+\frac{7}{4096}\cdot t$
• $P_3$:
  $8192\cdot t^{113}-233472\cdot t^{111}+3238912\cdot t^{109}-29145600\cdot t^{107}+191271488\cdot t^{105}-975866528\cdot t^{103}+4029415208\cdot t^{101}-13840359260\cdot t^{99}+\frac{80683847475}{2}\cdot t^{97}-\frac{405182905435}{4}\cdot t^{95}+\frac{3546775237005}{16}\cdot t^{93}-\frac{13654998106435}{32}\cdot t^{91}+\frac{186361217943537}{256}\cdot t^{89}-\frac{566958028866565}{512}\cdot t^{87}+\frac{3091332537306409}{2048}\cdot t^{85}-\frac{7583717723186987}{4096}\cdot t^{83}+\frac{1075137643173989911}{524288}\cdot t^{81}-\frac{2156590766035131183}{1048576}\cdot t^{79}+\frac{7852722592035679605}{4194304}\cdot t^{77}-\frac{13001372343447979491}{8388608}\cdot t^{75}+\frac{78419760059939853555}{67108864}\cdot t^{73}-\frac{107825462418329920935}{134217728}\cdot t^{71}+\frac{270609889049816602095}{536870912}\cdot t^{69}-\frac{310087994930505911925}{1073741824}\cdot t^{67}+\frac{649143766072600718715}{4294967296}\cdot t^{65}-\frac{620691884569961261343}{8589934592}\cdot t^{63}+\frac{1084095641917041042177}{34359738368}\cdot t^{61}-\frac{864305107047406491999}{68719476736}\cdot t^{59}+\frac{2514611124353468567025}{549755813888}\cdot t^{57}-\frac{1667088624698781174741}{1099511627776}\cdot t^{55}+\frac{2012385031454740125249}{4398046511104}\cdot t^{53}-\frac{1104192060639831108803}{8796093022208}\cdot t^{51}+\frac{35190532585279419734815}{1125899906842624}\cdot t^{49}-\frac{15871689009395138512775}{2251799813685248}\cdot t^{47}+\frac{12937081655910778736405}{9007199254740992}\cdot t^{45}-\frac{4751642275090749046995}{18014398509481984}\cdot t^{43}+\frac{6272004602479620139135}{144115188075855872}\cdot t^{41}-\frac{1853054551321765264179}{288230376151711744}\cdot t^{39}+\frac{976454591898212025235}{1152921504606846976}\cdot t^{37}-\frac{228386149945373659953}{2305843009213693952}\cdot t^{35}+\frac{188705766231962155351}{18446744073709551616}\cdot t^{33}-\frac{34222191359711666927}{36893488147419103232}\cdot t^{31}+\frac{10823665194297227657}{147573952589676412928}\cdot t^{29}-\frac{1480859113679264935}{295147905179352825856}\cdot t^{27}+\frac{694784554791889653}{2361183241434822606848}\cdot t^{25}-\frac{69121790122548345}{4722366482869645213696}\cdot t^{23}+\frac{11518464787252605}{18889465931478580854784}\cdot t^{21}-\frac{791650591278855}{37778931862957161709568}\cdot t^{19}+\frac{5639612435403975}{9671406556917033397649408}\cdot t^{17}-\frac{248417609161215}{19342813113834066795298816}\cdot t^{15}+\frac{16825609562133}{77371252455336267181195264}\cdot t^{13}-\frac{421789938531}{154742504910672534362390528}\cdot t^{11}+\frac{29736860043}{1237940039285380274899124224}\cdot t^9-\frac{342294975}{2475880078570760549798248448}\cdot t^7+\frac{4589431}{9903520314283042199192993792}\cdot t^5-\frac{14637}{19807040628566084398385987584}\cdot t^3+\frac{7}{19807040628566084398385987584}\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.