Rule: Q[8, 44]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{52}-\frac{115226258175118286568144571127163584880271861633382}{96463059700968922754665093508150590981130145789}\cdot t^{50}+\frac{52313244508889740714213761393081251988921042644370655}{79686875405148240536462468550211357767020555217}\cdot t^{48}-\frac{4985361614078026584433216046880202029094095344476713399400}{22604510323260384232176520245409955153244830829889}\cdot t^{46}+\frac{3442028043612710504524894831460119273706191583137117661693690}{67813530969781152696529560736229865459734492489667}\cdot t^{44}-\frac{44339261517591703883266270923022479155803289382605588329215380}{5216425459213934822809966210479220419979576345359}\cdot t^{42}+\frac{24275945864007914471289486091178107912714800342410894113193504090}{22604510323260384232176520245409955153244830829889}\cdot t^{40}-\frac{182171441631947708156090720725683204599215730728207371942960320200}{1738808486404644940936655403493073473326525448453}\cdot t^{38}+\frac{19814295124022451031281895361015854909360071327900900849707458825}{2473411787204331352683720346362835666182824251}\cdot t^{36}-\frac{1198893748227299119977481321707258649861315307961234507227699770950}{2473411787204331352683720346362835666182824251}\cdot t^{34}+\frac{57718816390549484217613344471506469256565877316485796880038193356575}{2473411787204331352683720346362835666182824251}\cdot t^{32}-\frac{2216040924268906519354236413652315974441041904177941514398361909919600}{2473411787204331352683720346362835666182824251}\cdot t^{30}+\frac{67819407524336399299224440707132046522140350902148275030692633712497500}{2473411787204331352683720346362835666182824251}\cdot t^{28}-\frac{1649443244741609665397110751734187340851609951403847886037417302374899000}{2473411787204331352683720346362835666182824251}\cdot t^{26}+\frac{31705556123174987710230940052077892533122186030999361367676645496626592500}{2473411787204331352683720346362835666182824251}\cdot t^{24}-\frac{20772621283230309396769417783466212301200099081500838981442201770775010000}{107539642921927450116683493320123289834035837}\cdot t^{22}+\frac{242700615335770043078164873449080812154894313735079048675367602262491576875}{107539642921927450116683493320123289834035837}\cdot t^{20}-\frac{2167115602536693453189596298084818625549394429235486845500619789374141956250}{107539642921927450116683493320123289834035837}\cdot t^{18}+\frac{14516117195517555526899294246948703395260283277237680915763660054383019003125}{107539642921927450116683493320123289834035837}\cdot t^{16}-\frac{71213835114955415637824474230271298233033697408354921386061727986382466025000}{107539642921927450116683493320123289834035837}\cdot t^{14}+\frac{247982562217042085024324498038267770547178087060159640680905971064215279993750}{107539642921927450116683493320123289834035837}\cdot t^{12}-\frac{587705386775209998094691789551363854446723949734295841293262388391853266637500}{107539642921927450116683493320123289834035837}\cdot t^{10}+\frac{893567440350813158290548122920199520170914440342163764840933926969321164781250}{107539642921927450116683493320123289834035837}\cdot t^8-\frac{797348770364747306866596767523524480984278769123583778270223118947850701625000}{107539642921927450116683493320123289834035837}\cdot t^6+\frac{359536782402768037026341710124257477019255355903710296381842369480696379265625}{107539642921927450116683493320123289834035837}\cdot t^4-\frac{60670719183040424379603193921048673655768498875330789548030588475801293593750}{107539642921927450116683493320123289834035837}\cdot t^2+\frac{1543883273673835963592062164167340794728377833051342048147041636825187109375}{107539642921927450116683493320123289834035837}$

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.