Manuscript Em01-E@2 · Em01-E-v2.tex · section · 54f8f8c2

Angular Taylor expansion and profile moments

Evaluated complete degenerate specialization › Angular Taylor expansion and profile moments · lines 1838–1851

Em01-E@2#eq:appLn

For $n \geq 0$ , define

L_{n} (B, S, T) = a + b + c = n a, b, c \geq 0 \sum \frac{( T /2 ) ^{a} ( S /2 ) ^{b} ( B T /2 ) ^{c}}{a ! b ! ( c ! ) ^{2}} \partial_{u}^{a} \partial_{v}^{b} Δ_{X}^{c} .

A subscript $0$ below means $u = v = X = 0$ .

Displayed formulas in this passage

Em01-E@2#eq:appLn · line 1841
$L_{n} (B, S, T) = a + b + c = n a, b, c \geq 0 \sum \frac{( T /2 ) ^{a} ( S /2 ) ^{b} ( B T /2 ) ^{c}}{a ! b ! ( c ! ) ^{2}} \partial_{u}^{a} \partial_{v}^{b} Δ_{X}^{c} .$