Rule: Q[24, 39]

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.

• $P_1$:
  $16777216\cdot t^{24}-2315255808\cdot t^{22}+133706022912\cdot t^{20}-4234024058880\cdot t^{18}+80975710126080\cdot t^{16}-971708521512960\cdot t^{14}+7368789621473280\cdot t^{12}-34738579644088320\cdot t^{10}+97702255248998400\cdot t^8-151981285942886400\cdot t^6+113985964457164800\cdot t^4-31087081215590400\cdot t^2+1295295050649600$
• $P_2$:
  $16777216\cdot t^{63}-\frac{18052092025020592833059501613923863873217101824}{1510048018601572117403227320260766503}\cdot t^{61}+\frac{150052464103018705319927209125793737825142563667968}{37751200465039302935080683006519162575}\cdot t^{59}-\frac{30973415820959381507770610503545932360165290068148224}{37751200465039302935080683006519162575}\cdot t^{57}+\frac{342706222036546669660445920121964268344036494228324352}{2903938497310715610390821769732243275}\cdot t^{55}-\frac{95030768448059904189450328286788959396128107737219858432}{7550240093007860587016136601303832515}\cdot t^{53}+\frac{1561476258599874281099515900314907795877839194196767670272}{1510048018601572117403227320260766503}\cdot t^{51}-\frac{506769855657269134538010342028653677337126311201226601660416}{7550240093007860587016136601303832515}\cdot t^{49}+\frac{26447683325166574447038813948648389200355157668408306986057728}{7550240093007860587016136601303832515}\cdot t^{47}-\frac{1123593219697942881416833748799831385835624235414860371046203392}{7550240093007860587016136601303832515}\cdot t^{45}+\frac{7839703069096505967332525154979181891045873931458602606300348416}{1510048018601572117403227320260766503}\cdot t^{43}-\frac{225949226829192389052190940129947025784751577530698546342753411072}{1510048018601572117403227320260766503}\cdot t^{41}+\frac{415438385133175955021912176785181885690408093568174073371838001152}{116157539892428624415632870789289731}\cdot t^{39}-\frac{8252274749063727477313839232994773514652271767401792318258110457856}{116157539892428624415632870789289731}\cdot t^{37}+\frac{136298019301294871106947147800720048354493789202007554049565402225664}{116157539892428624415632870789289731}\cdot t^{35}-\frac{1870041568151377556080402441555287510368143410282332022833025797460480}{116157539892428624415632870789289731}\cdot t^{33}+\frac{21264457186531141228175648889637552446934511847188346535697959954602240}{116157539892428624415632870789289731}\cdot t^{31}-\frac{199657685371840293624962168457089080001759690009105609848577019944803200}{116157539892428624415632870789289731}\cdot t^{29}+\frac{1539894567540341093403290514277272979049768848189161313905833577110126400}{116157539892428624415632870789289731}\cdot t^{27}-\frac{9689586257516091067174321814939044638653510559635706022411871566050261600}{116157539892428624415632870789289731}\cdot t^{25}+\frac{49312077760178575955912502322244524284220038456956860422514052869698210000}{116157539892428624415632870789289731}\cdot t^{23}-\frac{200768709644813579319263081941291028166326553099419786468529715788337167000}{116157539892428624415632870789289731}\cdot t^{21}+\frac{645074382709923879562834997194895985665750609258311833507589271094649870500}{116157539892428624415632870789289731}\cdot t^{19}-\frac{1607920473599923189420793475717325058875269020509849788221316986934377592750}{116157539892428624415632870789289731}\cdot t^{17}+\frac{3042597447560460313719574662837154234883172863301581338188432559986234724125}{116157539892428624415632870789289731}\cdot t^{15}-\frac{8500401519848579700989480420553431870521293647782994574147799652603719081875}{232315079784857248831265741578579462}\cdot t^{13}+\frac{16895079565528129109466456256861370250961344859296956484774680470819669070625}{464630159569714497662531483157158924}\cdot t^{11}-\frac{22707227585737486439951828246930157869875340715622291184219871099166287759375}{929260319139428995325062966314317848}\cdot t^9+\frac{19175156711431571808869328229222865573438096009221943318990249039932531640625}{1858520638278857990650125932628635696}\cdot t^7-\frac{9068509918891233709451080384914283469316796206820354612914263965363526559375}{3717041276557715981300251865257271392}\cdot t^5+\frac{45586592451464082201712359826725333658291524270004786629810068114350734375}{172885640770126324711639621639873088}\cdot t^3-\frac{122862490700363325562096551579474485114697396887964807033866758769290921875}{14868165106230863925201007461029085568}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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