Rule: Q[1, 66, 68]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{67}-\frac{67}{4}\cdot t^{65}+134\cdot t^{63}-\frac{43617}{64}\cdot t^{61}+\frac{633485}{256}\cdot t^{59}-\frac{6992857}{1024}\cdot t^{57}+\frac{15246721}{1024}\cdot t^{55}-\frac{215632197}{8192}\cdot t^{53}+\frac{2518145487}{65536}\cdot t^{51}-\frac{12301285425}{262144}\cdot t^{49}+\frac{6344873535}{131072}\cdot t^{47}-\frac{89075432355}{2097152}\cdot t^{45}+\frac{267226297065}{8388608}\cdot t^{43}-\frac{687479618945}{33554432}\cdot t^{41}+\frac{379874182975}{33554432}\cdot t^{39}-\frac{1443521895305}{268435456}\cdot t^{37}+\frac{9425348845815}{4294967296}\cdot t^{35}-\frac{13195488384141}{17179869184}\cdot t^{33}+\frac{987417498133}{4294967296}\cdot t^{31}-\frac{8055248011085}{137438953472}\cdot t^{29}+\frac{6958363175533}{549755813888}\cdot t^{27}-\frac{5056698705201}{2199023255552}\cdot t^{25}+\frac{766166470485}{2199023255552}\cdot t^{23}-\frac{766166470485}{17592186044416}\cdot t^{21}+\frac{623623871325}{140737488355328}\cdot t^{19}-\frac{203123203803}{562949953421312}\cdot t^{17}+\frac{6478601247}{281474976710656}\cdot t^{15}-\frac{5038912081}{4503599627370496}\cdot t^{13}+\frac{719844583}{18014398509481984}\cdot t^{11}-\frac{71853815}{72057594037927936}\cdot t^9+\frac{1165197}{72057594037927936}\cdot t^7-\frac{87703}{576460752303423488}\cdot t^5+\frac{12529}{18446744073709551616}\cdot t^3-\frac{67}{73786976294838206464}\cdot t$
• $P_3$:
  $t^{135}-34\cdot t^{133}+\frac{9043}{16}\cdot t^{131}-\frac{97955}{16}\cdot t^{129}+\frac{388763}{8}\cdot t^{127}-301371\cdot t^{125}+\frac{6227645025}{4096}\cdot t^{123}-\frac{26277194175}{4096}\cdot t^{121}+\frac{1513899380125}{65536}\cdot t^{119}-\frac{2361758083003}{32768}\cdot t^{117}+\frac{206775699101257}{1048576}\cdot t^{115}-\frac{500836914035029}{1048576}\cdot t^{113}+\frac{4329160072854617}{4194304}\cdot t^{111}-\frac{2100015603897085}{1048576}\cdot t^{109}+\frac{470831363819751429}{134217728}\cdot t^{107}-\frac{747840057850005831}{134217728}\cdot t^{105}+\frac{34599614690681960751}{4294967296}\cdot t^{103}-\frac{22842087253770687891}{2147483648}\cdot t^{101}+\frac{883829604857199821025}{68719476736}\cdot t^{99}-\frac{981002849858832000585}{68719476736}\cdot t^{97}+\frac{2003089133935106777175}{137438953472}\cdot t^{95}-\frac{58883809925645763135}{4294967296}\cdot t^{93}+\frac{104676165761768313596835}{8796093022208}\cdot t^{91}-\frac{83940734928296549045925}{8796093022208}\cdot t^{89}+\frac{995986313620727437167705}{140737488355328}\cdot t^{87}-\frac{341795574742332873741579}{70368744177664}\cdot t^{85}+\frac{6951993866309074277574257}{2251799813685248}\cdot t^{83}-\frac{4093979238240882147055829}{2251799813685248}\cdot t^{81}+\frac{8937346254148369269009735}{9007199254740992}\cdot t^{79}-\frac{1130250822075291050638413}{2251799813685248}\cdot t^{77}+\frac{67830709751579184701213769}{288230376151711744}\cdot t^{75}-\frac{29472179751212206770920235}{288230376151711744}\cdot t^{73}+\frac{759257802704172081313520055}{18446744073709551616}\cdot t^{71}-\frac{141505123205836452473952975}{9223372036854775808}\cdot t^{69}+\frac{1562043211705950587727519357}{295147905179352825856}\cdot t^{67}-\frac{498310861122401293283590749}{295147905179352825856}\cdot t^{65}+\frac{146878054673623593501537213}{295147905179352825856}\cdot t^{63}-\frac{4994793119260585622701707}{36893488147419103232}\cdot t^{61}+\frac{1282730765231366634067556685}{37778931862957161709568}\cdot t^{59}-\frac{296155015851873494222916483}{37778931862957161709568}\cdot t^{57}+\frac{1005555153472816897836872637}{604462909807314587353088}\cdot t^{55}-\frac{97894281302879540593563603}{302231454903657293676544}\cdot t^{53}+\frac{558523137026386324946993697}{9671406556917033397649408}\cdot t^{51}-\frac{90983631735686031281099325}{9671406556917033397649408}\cdot t^{49}+\frac{54032760118482207200416845}{38685626227668133590597632}\cdot t^{47}-\frac{1822812873728114665900125}{9671406556917033397649408}\cdot t^{45}+\frac{28527814001181398049452565}{1237940039285380274899124224}\cdot t^{43}-\frac{3149639696053767778809255}{1237940039285380274899124224}\cdot t^{41}+\frac{10009370231810563389140925}{39614081257132168796771975168}\cdot t^{39}-\frac{445145195808083558413665}{19807040628566084398385987584}\cdot t^{37}+\frac{1129271409588012420708459}{633825300114114700748351602688}\cdot t^{35}-\frac{79357641131331424623411}{633825300114114700748351602688}\cdot t^{33}+\frac{9825557167736212531959}{1267650600228229401496703205376}\cdot t^{31}-\frac{33254542526068356515}{79228162514264337593543950336}\cdot t^{29}+\frac{1599981366704409133137}{81129638414606681695789005144064}\cdot t^{27}-\frac{64618066510726248247}{81129638414606681695789005144064}\cdot t^{25}+\frac{35500482823706330935}{1298074214633706907132624082305024}\cdot t^{23}-\frac{511541522850391885}{649037107316853453566312041152512}\cdot t^{21}+\frac{389879375295255175}{20769187434139310514121985316880384}\cdot t^{19}-\frac{7532424265746579}{20769187434139310514121985316880384}\cdot t^{17}+\frac{461394459237477}{83076749736557242056487941267521536}\cdot t^{15}-\frac{1359786276051}{20769187434139310514121985316880384}\cdot t^{13}+\frac{1520451953111}{2658455991569831745807614120560689152}\cdot t^{11}-\frac{9346696645}{2658455991569831745807614120560689152}\cdot t^9+\frac{4806337393}{340282366920938463463374607431768211456}\cdot t^7-\frac{5625521}{170141183460469231731687303715884105728}\cdot t^5+\frac{200531}{5444517870735015415413993718908291383296}\cdot t^3-\frac{67}{5444517870735015415413993718908291383296}\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.