Rule: Q[29, 30, 58]

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.

• $P_1$:
  $268435456\cdot t^{29}-1946157056\cdot t^{27}+6325010432\cdot t^{25}-12163481600\cdot t^{23}+15386804224\cdot t^{21}-13463453696\cdot t^{19}+8341487616\cdot t^{17}-3683254272\cdot t^{15}+1151016960\cdot t^{13}-249387008\cdot t^{11}+36095488\cdot t^9-3281408\cdot t^7+168896\cdot t^5-4060\cdot t^3+29\cdot t$
• $P_2$:
  $268435456\cdot t^{59}-4026531840\cdot t^{57}+28672262144\cdot t^{55}-128949682176\cdot t^{53}+411084783616\cdot t^{51}-988351037440\cdot t^{49}+1861569740800\cdot t^{47}-2816773980160\cdot t^{45}+3483712167936\cdot t^{43}-3564563357696\cdot t^{41}+3042942287616\cdot t^{39}-2179395212800\cdot t^{37}+1313970472464\cdot t^{35}-667822453648\cdot t^{33}+286041066088\cdot t^{31}-103047067264\cdot t^{29}+\frac{248883578585}{8}\cdot t^{27}-\frac{62630270703}{8}\cdot t^{25}+\frac{208644329595}{128}\cdot t^{23}-\frac{17798864985}{64}\cdot t^{21}+\frac{78643211955}{2048}\cdot t^{19}-\frac{8648672175}{2048}\cdot t^{17}+\frac{2968493505}{8192}\cdot t^{15}-\frac{48370695}{2048}\cdot t^{13}+\frac{295739535}{262144}\cdot t^{11}-\frac{9852141}{262144}\cdot t^9+\frac{13633335}{16777216}\cdot t^7-\frac{85463}{8388608}\cdot t^5+\frac{16269}{268435456}\cdot t^3-\frac{29}{268435456}\cdot t$
• $P_3$:
  $268435456\cdot t^{117}-7918845952\cdot t^{115}+113816633344\cdot t^{113}-1062131990528\cdot t^{111}+7235892674560\cdot t^{109}-38364130050048\cdot t^{107}+164796134326272\cdot t^{105}-589550577647616\cdot t^{103}+1791928440819712\cdot t^{101}-4697769229670400\cdot t^{99}+10747884836648960\cdot t^{97}-21660072118630400\cdot t^{95}+38741164720740160\cdot t^{93}-61878355630068320\cdot t^{91}+88709542803747600\cdot t^{89}-114632103014619960\cdot t^{87}+\frac{1071938406899639433}{8}\cdot t^{85}-\frac{2273472876510702979}{16}\cdot t^{83}+\frac{1096298929821118319}{8}\cdot t^{81}-\frac{3854024643152097585}{32}\cdot t^{79}+\frac{395749839891050742591}{4096}\cdot t^{77}-\frac{580347311764558892697}{8192}\cdot t^{75}+\frac{778639135365921340485}{16384}\cdot t^{73}-\frac{956503564762097499615}{32768}\cdot t^{71}+\frac{17221448552899127907825}{1048576}\cdot t^{69}-\frac{17756282864539735943859}{2097152}\cdot t^{67}+\frac{8387464681021308981813}{2097152}\cdot t^{65}-\frac{1814746751785365325653}{1048576}\cdot t^{63}+\frac{23010883367965770790077}{33554432}\cdot t^{61}-\frac{16687945082145171507555}{67108864}\cdot t^{59}+\frac{11065445090200941450573}{134217728}\cdot t^{57}-\frac{6701266157318565703059}{268435456}\cdot t^{55}+\frac{236902548959840841867801}{34359738368}\cdot t^{53}-\frac{119168812666195488210339}{68719476736}\cdot t^{51}+\frac{6811232805085882700475}{17179869184}\cdot t^{49}-\frac{11299927283480553230695}{137438953472}\cdot t^{47}+\frac{135704577767469390190875}{8796093022208}\cdot t^{45}-\frac{45955398101854989432685}{17592186044416}\cdot t^{43}+\frac{13998507342786209454365}{35184372088832}\cdot t^{41}-\frac{3821869782769019917775}{70368744177664}\cdot t^{39}+\frac{14903082979514340095555}{2251799813685248}\cdot t^{37}-\frac{3227311204861414202553}{4503599627370496}\cdot t^{35}+\frac{308874754585438175337}{4503599627370496}\cdot t^{33}-\frac{25973508769669269039}{4503599627370496}\cdot t^{31}+\frac{60989345627546597905}{144115188075855872}\cdot t^{29}-\frac{7748983278779296127}{288230376151711744}\cdot t^{27}+\frac{844562001782884749}{576460752303423488}\cdot t^{25}-\frac{78116253084912315}{1152921504606846976}\cdot t^{23}+\frac{193730189592034095}{73786976294838206464}\cdot t^{21}-\frac{12390283861966725}{147573952589676412928}\cdot t^{19}+\frac{160486670266299}{73786976294838206464}\cdot t^{17}-\frac{13166182157787}{295147905179352825856}\cdot t^{15}+\frac{53163225505719}{75557863725914323419136}\cdot t^{13}-\frac{1241723809281}{151115727451828646838272}\cdot t^{11}+\frac{20395658965}{302231454903657293676544}\cdot t^9-\frac{218818079}{604462909807314587353088}\cdot t^7+\frac{21878557}{19342813113834066795298816}\cdot t^5-\frac{65047}{38685626227668133590597632}\cdot t^3+\frac{29}{38685626227668133590597632}\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.