Rule: Q[4, 53]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{57}-\frac{29908483841498755012015840173067704877477849464}{2452070369646233148101113457952700592074375}\cdot t^{55}+\frac{519118801831427020314611944071262819854683860089408}{120151448112665424256954559439682329011644375}\cdot t^{53}-\frac{113609340376506383730068481524194193836704397909366002}{120151448112665424256954559439682329011644375}\cdot t^{51}+\frac{689204639176661967004010848285006854123489954569297433}{4806057924506616970278182377587293160465775}\cdot t^{49}-\frac{1571736236545774555902249715963546275271769424827212797}{98082814785849325924044538318108023682975}\cdot t^{47}+\frac{134328502563941957969341685914251687817983856554439369752}{98082814785849325924044538318108023682975}\cdot t^{45}-\frac{35987866979363248933512035779656260794006247621094141806439}{392331259143397303696178153272432094731900}\cdot t^{43}+\frac{7681196484177677448722115021066351333179038919597442061684119}{1569325036573589214784712613089728378927600}\cdot t^{41}-\frac{132081100422742762228970186490994270666206014855685257194833633}{627730014629435685913885045235891351571040}\cdot t^{39}+\frac{144008698214986407107840439975998076184204288494437619227548449}{19616562957169865184808907663621604736595}\cdot t^{37}-\frac{524305775818059519489424649759267118515056145279269577097941063343}{2510920058517742743655540180943565406284160}\cdot t^{35}+\frac{24366565754024542399946839304530554594169843944638856386298259261893}{5021840117035485487311080361887130812568320}\cdot t^{33}-\frac{231281619097837737850771304625028479755159025171287683570713678278811}{2510920058517742743655540180943565406284160}\cdot t^{31}+\frac{11187483260321822900924011285475898759924953695587775920855360369213}{7846625182867946073923563065448641894638}\cdot t^{29}-\frac{36010022594623905745059170083367044795545482725720897595255343625097253}{2008736046814194194924432144754852325027328}\cdot t^{27}+\frac{2925258296499224360798384470215148186776443200636796944688276230106444685}{16069888374513553559395457158038818600218624}\cdot t^{25}-\frac{47598962689173461933335731958732894101587545362888563745629576150575766985}{32139776749027107118790914316077637200437248}\cdot t^{23}+\frac{38382956331864949961790342455889413069281024043967920525060752547202822405}{4017472093628388389848864289509704650054656}\cdot t^{21}-\frac{6199101455615213327568631954207019595541967780606181462066659171582072237775}{128559106996108428475163657264310548801748992}\cdot t^{19}+\frac{48125184607085459638407602219682641533826405637366801795466718718970412967675}{257118213992216856950327314528621097603497984}\cdot t^{17}-\frac{140545092341828827407684707058671485166070681675911027468723334547129487460525}{257118213992216856950327314528621097603497984}\cdot t^{15}+\frac{37513646931597548140587902131491560872300657147784106055396521309048441245025}{32139776749027107118790914316077637200437248}\cdot t^{13}-\frac{1804369658899207402070554705931071440467154459831057087510169402742738840845575}{1028472855968867427801309258114484390413991936}\cdot t^{11}+\frac{7247947264735037025073328547528886088855061820657379766651998153267808462274125}{4113891423875469711205237032457937561655967744}\cdot t^9-\frac{9019065417719865757945641029483907669254906708187912205195715531218103545108875}{8227782847750939422410474064915875123311935488}\cdot t^7+\frac{193212716566128761734257092869846320710186925935559481761502746661572768011475}{514236427984433713900654629057242195206995968}\cdot t^5-\frac{1897945078608167609349683393488942288554765156353235921551811985119140078546325}{32911131391003757689641896259663500493247741952}\cdot t^3+\frac{163077940747771505123925641765563019736507960416332684540919985583616370623475}{65822262782007515379283792519327000986495483904}\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.