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@Article{ a-sample, author = {J{\"u}rgen Prestin and Daniela Ro\c{s}ca}, title = {On some cubature formulas on the sphere}, journal = {J. Approximation Theory}, year = 2019, volume = 2, number = 1, pages = {11-22}, month = mar, abstract = {We construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Laín Fernández [Polynomial Bases on the Sphere, Logos-Verlag, Berlin, 2003; Localized polynomial bases on the sphere, Electron. Trans. Numer. Anal. 19 (2005) 84–93]. \\ \\ {\bf Functions:} \\ \cosh x, {\hbox{cosh}} x \\ \tanh x, {\hbox{tanh}} x \\ \sinh x, {\hbox{sinh}} x \\ \sup x, {\hbox{sup}} x \\ \cos x, {\hbox{cos}} x \\ \tan x, {\hbox{tan}} x \\ \sin x, {\hbox{sin}} x \\ {x\over y}, over (division) \\ {\bf Plain text accents (TeXbook, p. 52):}\\ \; \'a\; \'e\; \'i\; \'j\; \'o\; \'u\; \'x\; \'A\; \'E\; \'I\; \'O\; \'U\; \'X \quad \backslash ', grave accent\\ \; \`a\; \`e\; \`i\; \`j\; \`o\; \`u\; \`x\; \`A\; \`E\; \`I\; \`O\; \`U\; \`X \quad \backslash `, acute accent\\ \; \^a\; \^e\; \^i\; \^j\; \^o\; \^u\; \^x\; \^A\; \^E\; \^I\; \^O\; \^U\; \^X \quad \backslash ^, circumflex or hat\\ \; \"a\; \"e\; \"i\; \"j\; \"o\; \"u\; \"x\; \"A\; \"E\; \"I\; \"O\; \"U\; \"X \quad \backslash ", umlaut or dieresis\\ \; \~a\; \~e\; \~i\; \~j\; \~o\; \~u\; \~x\; \~A\; \~E\; \~I\; \~O\; \~U\; \~X \quad tilde\\ \; \=a\; \=e\; \=i\; \=j\; \=o\; \=u\; \=x\; \=A\; \=E\; \=I\; \=O\; \=U\; \=X \quad \backslash =, macron or bar\\ \u a \u e \u i \u j \u o \u u \u x \u A \u E \u I \u O \u U \u X \quad \backslash u, breve accent\\ \v a \v e \v i \v j \v o \v u \v x \v A \v E \v I \v O \v U \v X \quad \backslash v, hacek or "check"\\ \H a \H e \H i \H j \H o \H u \H x \H A \H E \H I \H O \H U \H X \quad \backslash H, long Hungarian umlaut\\ \; \.a\; \.e\; \qquad \qquad \.o\; \.u\; \.x\; \.A\; \.E\ \.I\; \.O\; \.U\; \.X \quad \backslash ., dot accent\\ \;\t xy \quad \backslash t, tie-after accent \\ \c a \c b \c c \c d \c e \c f \c g \c h \c i \c j \c k \c l \c m \c n \c o \c p \c q \c r \c s \c t \c u \c v \c w \c x \c y \c z , cedilla accent \\ \d a \d b \d c \d d \d e \d f \d g \d h \d i \d j \d k \d l \d m \d n \d o \d p \d q \d r \d s \d t \d u \d v \d w \d x \d y \d z , dot-under \\ \b a \b b \b c \b d \b e \b f \b g \b h \b i \b j \b k \b l \b m \b n \b o \b p \b q \b r \b s \b t \b u \b v \b w \b x \b y \b z , bar-under accent \\ \c A \c B \c C \c D \c E \c F \c G \c H \c I \c J \c K \c L \c M \c N \c O \c P \c Q \c R \c S \c T \c U \c V \c W \c X \c Y \c Z , cedilla accent \\ \d A \d B \d C \d D \d E \d F \d G \d H \d I \d J \d K \d L \d M \d N \d O \d P \d Q \d R \d S \d T \d U \d V \d W \d X \d Y \d Z , dot-under \\ \b A \b B \b C \b D \b E \b F \b G \b H \b I \b J \b K \b L \b M \b N \b O \b P \b Q \b R \b S \b T \b U \b V \b W \b X \b Y \b Z , bar-under accent \\ {\bf Math accents (TeXbook, p. 135):}\\ $\quad \hat a\quad \hat e\quad \hat i\quad \hat j\quad \hat o\quad \hat u\quad \hat x\quad \hat A\quad \hat E\quad \hat I\quad \hat O\quad \hat U\quad \hat X $ hat\\ $\quad \dot a\quad \dot e\quad \dot i\quad \dot j\quad \dot o\quad \dot u\quad \dot x\quad \dot A\quad \dot E\quad \dot I\quad \dot O\quad \dot U\quad \dot X $ dot\\ $\quad \bar a\quad \bar e\quad \bar i\quad \bar j\quad \bar o\quad \bar u\quad \bar x\quad \bar A\quad \bar E\quad \bar I\quad \bar O\quad \bar U\quad \bar X $ bar\\ $\quad \vec a\quad \vec e\quad \vec i\quad \vec j\quad \vec o\quad \vec u\quad \vec x\quad \vec A\quad \vec E\quad \vec I\quad \vec O\quad \vec U\quad \vec X $ vec\\ $\quad \ddot a\quad \ddot e\quad \ddot i\quad \ddot j\quad \ddot o\quad \ddot u\quad \ddot x\quad \ddot A\quad \ddot E\quad \ddot I\quad \ddot O\quad \ddot U\quad \ddot X $ ddot\\ $\quad \check a\quad \check e\quad \check i\quad \check j\quad \check o\quad \check u\quad \check x\quad \check A\quad \check E\quad \check I\quad \check O\quad \check U\quad \check X $ check\\ $\quad \tilde a\quad \tilde e\quad \tilde i\quad \tilde j\quad \tilde o\quad \tilde u\quad \tilde x\quad \tilde A\quad \tilde E\quad \tilde I\quad \tilde O\quad \tilde U\quad \tilde X $ tilde\\ $\quad \acute a\quad \acute e\quad \acute i\quad \acute j\quad \acute o\quad \acute u\quad \acute x\quad \acute A\quad \acute E\quad \acute I\quad \acute O\quad \acute U\quad \acute X $ acute\\ $\quad \grave a\quad \grave e\quad \grave i\quad \grave j\quad \grave o\quad \grave u\quad \grave x\quad \grave A\quad \grave E\quad \grave I\quad \grave O\quad \grave U\quad \grave X $ grave\\ $\quad \breve a\quad \breve e\quad \breve i\quad \breve j\quad \breve o\quad \breve u\quad \breve x\quad \breve A\quad \breve E\quad \breve I\quad \breve O\quad \breve U\quad \breve X $ breve\\ {\bf Other math accents}\\ $\quad \overbar i\quad \overbar j\quad \overbar x\quad \overbar X$ overbar \\ $\quad \overleftarrow i\quad \overleftarrow j\quad \overleftarrow x\quad \overleftarrow X$ overleftarrow\\ $\quad \overrightarrow i\quad \overrightarrow j\quad \overrightarrow x\quad \overrightarrow X$ overrightarrow \\ {\bf Special characters:} \\ \int dx, integral, U+222b \\ \sum x, sum, U+2211 \\ \prod x, product, U+220f \\ \ll, {≪} much less than, U+226a \\ \gg, {≫} much greater than, U+226b \\ \ell, {ℓ} script l, U+2113 \\ \langle, {⟨} left angle bracket, U+27e8 \\ \lbrace, {{} left brace, U+ff5b \\ \rbrace, {}} right brace, U+ff5d \\ \neg, not (\backslash neg) \\ \ddagger, double dagger \\ \infty, infinity \\ \angle, angle \\ \div, divide \\ x\quad x, \backslash quad \\ x\qquad x, \backslash qquad \\ \spadesuit, spade suit \\ \heartsuit, heart suit \\ \diamondsuit, diamond suit \\ \clubsuit, club suit \\ \flat, flat note \\ \natural, natural note \\ \sharp, sharp note \\ \leftarrow, left arrow \\ \uparrow, up arrow \\ \rightarrow, right arrow \\ \downarrow, down arrow \\ \leftrightarrow, left right arrow \\ \updownarrow, up down arrow \\ \nwarrow, northwest arrow \\ \nearrow, northeast arrow \\ \searrow, southeast arrow \\ \swarrow, southwest arrow \\ \mapsto, maps to \\ \star, star \\ \odot, o dot \\ \bigtriangleup, big triangle up \\ \bigtriangleright, big triangle right \\ \bigtriangledown, big triangle down \\ \bigtriangleleft, big triangle left \\ \amalg, amalg \\ \prime, prime not superscripted \\ \surd, surd \\ \top, top \\ \bot, bot \\ \hookleftarrow, hook left arrow \\ \hookrightarrow, hook right arrow \\ \leftharpoonup, left harpoon up \\ \leftharpoondown, left harpoon down \\ \rightharpoonup, right harpoon up \\ \rightharpoondown, right harpoon down \\ \Leftarrow, left double arrow \\ \Uparrow, up double arrow \\ \Rightarrow, right double arrow \\ \Downarrow, down double arrow \\ \approx, approx \\ \asymp, asymptotically equal to \\ \parallel, parallel \\ \equiv, identical with \\ \le, \leq, less than or equal \\ \ge, \geq, greater than or equal \\ \ll, much less than \\ \gg, much greater than \\ \prec, precedes \\ \succ, succeeds \\ \subset, subset or is implied by \\ \supset, superset or implies \\ \subseteq, subset, equals \\ \supseteq, superset, equals \\ \sqsubseteq, square subset, equals \\ \sqsupseteq, square superset, equals \\ \vdash, vertical, dash \\ \dashv, dash, vertical \\ \bowtie, bowtie \\ \vdots, vertical ellipsis \\ \ddots, three dots, descending \\ \frown, down curve (frown) \\ \smile, up curve (smile) \\ \perp, perpendicular \\ \longleftarrow, long left arrow \\ \longrightarrow, long right arrow \\ \longleftrightarrow, long left-right arrow \\ \Longleftarrow, double long left arrow \\ \Longrightarrow, double long right arrow \\ \Longleftrightarrow, double long left-right arrow \\ \Im, imaginary part \\ \wp, weierstrass p \\ \Re, real part \\ \aleph, aleph, Hebrew \\ \partial, partial \\ \nabla, nabla, del, Hamilton operator \\ \imath, math italic small dotless i \\ \jmath, math italic small dotless j \\ } } % % Unicode characters with combining class ``above''.\\ % \overleftarrow#1, {#1⃖} over left arrow U+20d6 \\ % \overrightarrow#1, {#1⃗} over right arrow U+20d7 \\ % \bar#1, {#1̅} overbar accent U+0305 \\ % \tilde#1, {#1̃} tilde accent U+0303 \\ % % no reasonable equivalence % \choose, {} preceding part over following part, in parens % \lower, {} lower a box