Gold 52

Kelvin functions

Gold ID

52

Link

https://sigir21.wmflabs.org/wiki/Kelvin_functions#math.103.8

Formula

$g_{1}(x)=\sum _{k\geq 1}{\frac {\sin(k\pi /4)}{k!(8x)^{k}}}\prod _{l=1}^{k}(2l-1)^{2}$

TeX Source

g_1(x) = \sum_{k \geq 1} \frac{\sin(k \pi / 4)}{k! (8x)^k} \prod_{l = 1}^k (2l - 1)^2

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

g_1(x) = \sum_{k \geq 1} \frac{\sin(k \cpi / 4)}{k! (8x)^k} \prod_{l = 1}^k(2 l - 1)^2

Expected (Gold Entry)

g_1(x) = \sum_{k \geq 1} \frac{\sin(k \cpi / 4)}{k! (8x)^k} \prod_{l = 1}^k(2 l - 1)^2

Mathematica

Translation

Subscript[g, 1][x] == Sum[Divide[Sin[k*Pi/4],(k)!*(8*x)^(k)]*Product[(2*l - 1)^(2), {l, 1, k}, GenerateConditions->None], {k, 1, Infinity}, GenerateConditions->None]

Expected (Gold Entry)

Subscript[g, 1][x_] := Sum[Divide[Sin[k*Pi/4],(k)!*(8*x)^(k)]*Product[(2*l - 1)^(2), {l, 1, k}], {k, 1, Infinity}]

Maple

Translation

g[1](x) = sum((sin(k*Pi/4))/(factorial(k)*(8*x)^(k))*product((2*l - 1)^(2), l = 1..k), k = 1..infinity)

Expected (Gold Entry)

g[1] := (x) -> sum((sin(k*Pi/4))/(factorial(k)*(8*x)^(k))*product((2*l - 1)^(2), l = 1..k), k = 1..infinity)