Rule: Q[40, 80]

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.

• $P_1$:
  $549755813888\cdot t^{40}-5497558138880\cdot t^{38}+25426206392320\cdot t^{36}-72155450572800\cdot t^{34}+140552804761600\cdot t^{32}-199183403319296\cdot t^{30}+212364657950720\cdot t^{28}-173752901959680\cdot t^{26}+110292369408000\cdot t^{24}-54553214976000\cdot t^{22}+21002987765760\cdot t^{20}-6254808268800\cdot t^{18}+1424085811200\cdot t^{16}-243433472000\cdot t^{14}+30429184000\cdot t^{12}-2677768192\cdot t^{10}+156900480\cdot t^8-5617920\cdot t^6+106400\cdot t^4-800\cdot t^2+1$
• $P_2$:
  $549755813888\cdot t^{120}-16492674416640\cdot t^{118}+241205363343360\cdot t^{116}-2291794549145600\cdot t^{114}+15906733503283200\cdot t^{112}-85979352570789888\cdot t^{110}+376788171536465920\cdot t^{108}-1376158062666055680\cdot t^{106}+4273615858669977600\cdot t^{104}-11456199468987187200\cdot t^{102}+26823128847615000576\cdot t^{100}-55368843951498854400\cdot t^{98}+101530908681124249600\cdot t^{96}-166420181015789568000\cdot t^{94}+245088480869277696000\cdot t^{92}-325695359021840138240\cdot t^{90}+391950094015165190400\cdot t^{88}-428436596199329625600\cdot t^{86}+426453093439147544000\cdot t^{84}-387341189090377368000\cdot t^{82}+321590022242285809782\cdot t^{80}-244402229505921875640\cdot t^{78}+170208695548767020535\cdot t^{76}-108716894288208428625\cdot t^{74}+\frac{32627147941383440635125}{512}\cdot t^{72}-\frac{8778420014544849922461}{256}\cdot t^{70}+\frac{34697028371728007467665}{2048}\cdot t^{68}-\frac{15738715776741617087085}{2048}\cdot t^{66}+\frac{209686617025532724545325}{65536}\cdot t^{64}-\frac{5005781308301842230525}{4096}\cdot t^{62}+\frac{14023603635553753567293}{32768}\cdot t^{60}-\frac{4498328821118184815895}{32768}\cdot t^{58}+\frac{675976140118941772788585}{16777216}\cdot t^{56}-\frac{90648141395260390986975}{8388608}\cdot t^{54}+\frac{177452107163635594394475}{67108864}\cdot t^{52}-\frac{39546469596467361036483}{67108864}\cdot t^{50}+\frac{256319710347473636347575}{2147483648}\cdot t^{48}-\frac{11768505098988532310325}{536870912}\cdot t^{46}+\frac{15635947082738293891125}{4294967296}\cdot t^{44}-\frac{2341184859175439382875}{4294967296}\cdot t^{42}+\frac{80630406550002132346215}{1099511627776}\cdot t^{40}-\frac{4854254176366290771075}{549755813888}\cdot t^{38}+\frac{4166716344304642749775}{4398046511104}\cdot t^{36}-\frac{396410645864078062875}{4398046511104}\cdot t^{34}+\frac{1064049628371999010875}{140737488355328}\cdot t^{32}-\frac{9773492882824287211}{17592186044416}\cdot t^{30}+\frac{4995851238576457035}{140737488355328}\cdot t^{28}-\frac{275201365226158665}{140737488355328}\cdot t^{26}+\frac{3312609025870428375}{36028797018963968}\cdot t^{24}-\frac{65699920317637125}{18014398509481984}\cdot t^{22}+\frac{17344778963856201}{144115188075855872}\cdot t^{20}-\frac{468244956398505}{144115188075855872}\cdot t^{18}+\frac{324169585198965}{4611686018427387904}\cdot t^{16}-\frac{1369344910725}{1152921504606846976}\cdot t^{14}+\frac{139854530725}{9223372036854775808}\cdot t^{12}-\frac{1290964899}{9223372036854775808}\cdot t^{10}+\frac{8299060065}{9444732965739290427392}\cdot t^8-\frac{16177505}{4722366482869645213696}\cdot t^6+\frac{269925}{37778931862957161709568}\cdot t^4-\frac{225}{37778931862957161709568}\cdot t^2+\frac{1}{1208925819614629174706176}$

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.