Rule: Q[28, 29, 56]

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.

• $P_1$:
  $134217728\cdot t^{28}-939524096\cdot t^{26}+2936012800\cdot t^{24}-5402263552\cdot t^{22}+6499598336\cdot t^{20}-5369233408\cdot t^{18}+3111714816\cdot t^{16}-1270087680\cdot t^{14}+361181184\cdot t^{12}-69701632\cdot t^{10}+8712704\cdot t^8-652288\cdot t^6+25480\cdot t^4-392\cdot t^2+1$
• $P_2$:
  $134217728\cdot t^{57}-1946157056\cdot t^{55}+13371441152\cdot t^{53}-57906561024\cdot t^{51}+177366630400\cdot t^{49}-408729681920\cdot t^{47}+735931793408\cdot t^{45}-1061391040512\cdot t^{43}+1247178307584\cdot t^{41}-1208087710720\cdot t^{39}+972422733568\cdot t^{37}-653762824832\cdot t^{35}+368128278336\cdot t^{33}-173746888672\cdot t^{31}+68657538920\cdot t^{29}-22648244492\cdot t^{27}+\frac{99306320607}{16}\cdot t^{25}-\frac{44906546835}{32}\cdot t^{23}+\frac{33199301355}{128}\cdot t^{21}-\frac{9911003025}{256}\cdot t^{19}+\frac{4704741195}{1024}\cdot t^{17}-\frac{869984775}{2048}\cdot t^{15}+\frac{244091985}{8192}\cdot t^{13}-\frac{25068615}{16384}\cdot t^{11}+\frac{114824775}{2097152}\cdot t^9-\frac{5330403}{4194304}\cdot t^7+\frac{286839}{16777216}\cdot t^5-\frac{3661}{33554432}\cdot t^3+\frac{7}{33554432}\cdot t$
• $P_3$:
  $134217728\cdot t^{113}-3825205248\cdot t^{111}+53066334208\cdot t^{109}-477521510400\cdot t^{107}+3133792059392\cdot t^{105}-15988597194752\cdot t^{103}+66017938767872\cdot t^{101}-226760446115840\cdot t^{99}+660962078515200\cdot t^{97}-1659629180661760\cdot t^{95}+3631897842693120\cdot t^{93}-6991359030494720\cdot t^{91}+11927117948386368\cdot t^{89}-18142656923730080\cdot t^{87}+24730660298451272\cdot t^{85}-30334870892747948\cdot t^{83}+\frac{1075137643173989911}{32}\cdot t^{81}-\frac{2156590766035131183}{64}\cdot t^{79}+\frac{7852722592035679605}{256}\cdot t^{77}-\frac{13001372343447979491}{512}\cdot t^{75}+\frac{78419760059939853555}{4096}\cdot t^{73}-\frac{107825462418329920935}{8192}\cdot t^{71}+\frac{270609889049816602095}{32768}\cdot t^{69}-\frac{310087994930505911925}{65536}\cdot t^{67}+\frac{649143766072600718715}{262144}\cdot t^{65}-\frac{620691884569961261343}{524288}\cdot t^{63}+\frac{1084095641917041042177}{2097152}\cdot t^{61}-\frac{864305107047406491999}{4194304}\cdot t^{59}+\frac{2514611124353468567025}{33554432}\cdot t^{57}-\frac{1667088624698781174741}{67108864}\cdot t^{55}+\frac{2012385031454740125249}{268435456}\cdot t^{53}-\frac{1104192060639831108803}{536870912}\cdot t^{51}+\frac{35190532585279419734815}{68719476736}\cdot t^{49}-\frac{15871689009395138512775}{137438953472}\cdot t^{47}+\frac{12937081655910778736405}{549755813888}\cdot t^{45}-\frac{4751642275090749046995}{1099511627776}\cdot t^{43}+\frac{6272004602479620139135}{8796093022208}\cdot t^{41}-\frac{1853054551321765264179}{17592186044416}\cdot t^{39}+\frac{976454591898212025235}{70368744177664}\cdot t^{37}-\frac{228386149945373659953}{140737488355328}\cdot t^{35}+\frac{188705766231962155351}{1125899906842624}\cdot t^{33}-\frac{34222191359711666927}{2251799813685248}\cdot t^{31}+\frac{10823665194297227657}{9007199254740992}\cdot t^{29}-\frac{1480859113679264935}{18014398509481984}\cdot t^{27}+\frac{694784554791889653}{144115188075855872}\cdot t^{25}-\frac{69121790122548345}{288230376151711744}\cdot t^{23}+\frac{11518464787252605}{1152921504606846976}\cdot t^{21}-\frac{791650591278855}{2305843009213693952}\cdot t^{19}+\frac{5639612435403975}{590295810358705651712}\cdot t^{17}-\frac{248417609161215}{1180591620717411303424}\cdot t^{15}+\frac{16825609562133}{4722366482869645213696}\cdot t^{13}-\frac{421789938531}{9444732965739290427392}\cdot t^{11}+\frac{29736860043}{75557863725914323419136}\cdot t^9-\frac{342294975}{151115727451828646838272}\cdot t^7+\frac{4589431}{604462909807314587353088}\cdot t^5-\frac{14637}{1208925819614629174706176}\cdot t^3+\frac{7}{1208925819614629174706176}\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.