Rule: Q[4, 45]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{49}-\frac{192242686175104680264709912002749643}{177036531294596661352651300338773}\cdot t^{47}+\frac{3920982342577665816618725850213749451714}{7258497783078463115458703313889693}\cdot t^{45}-\frac{1186702874162973090656914567924403496259695}{7258497783078463115458703313889693}\cdot t^{43}+\frac{34965454477640133000074576736527867030969970}{1036928254725494730779814759127099}\cdot t^{41}-\frac{127247659754142243730128142495189565478602655}{25290933042085237336093042905539}\cdot t^{39}+\frac{14232411242774429989702588509821069370586119030}{25290933042085237336093042905539}\cdot t^{37}-\frac{1220198608672994909977428334590228588078095557515}{25290933042085237336093042905539}\cdot t^{35}+\frac{81324391553517566590936800966531494909763308536725}{25290933042085237336093042905539}\cdot t^{33}-\frac{4249136329214965214325472664290569624681192908706450}{25290933042085237336093042905539}\cdot t^{31}+\frac{174767894158207184678046979505125137679628691841998300}{25290933042085237336093042905539}\cdot t^{29}-\frac{5661932228281337298918192411156070964994159272959105050}{25290933042085237336093042905539}\cdot t^{27}+\frac{144111860120839583188629501234677313799067335938753999900}{25290933042085237336093042905539}\cdot t^{25}-\frac{2865665932269094068017066897179861738999385407814174808750}{25290933042085237336093042905539}\cdot t^{23}+\frac{44127304372998175719611360772170250957520393261334407717500}{25290933042085237336093042905539}\cdot t^{21}-\frac{519697893625352087523106388526405335496031515349042489863750}{25290933042085237336093042905539}\cdot t^{19}+\frac{4603751540668158721607946838813222071680194616838732863998125}{25290933042085237336093042905539}\cdot t^{17}-\frac{30007910595611815205288734318782151561744497850917476123750625}{25290933042085237336093042905539}\cdot t^{15}+\frac{139812544175308898719589604422381223373947184313968173025443750}{25290933042085237336093042905539}\cdot t^{13}-\frac{448052262212855383779882714893668301507279472013641326525653125}{25290933042085237336093042905539}\cdot t^{11}+\frac{937379897779636255634643891060860850619149845687381610045581250}{25290933042085237336093042905539}\cdot t^9-\frac{1189917545610040054649328395141714403404856090350855364239971875}{25290933042085237336093042905539}\cdot t^7+\frac{822043198741113219480660792446736245311746276691689335828868750}{25290933042085237336093042905539}\cdot t^5-\frac{3261050198515998960740257038511926601880901339443975128640625}{320138392937787814380924593741}\cdot t^3+\frac{24309741925743407605982199737485515009888509581513105291546875}{25290933042085237336093042905539}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.