Gold 95

Incomplete Bessel K function/generalized incomplete gamma function

Gold ID

95

Link

https://sigir21.wmflabs.org/wiki/Incomplete_Bessel_K_function/generalized_incomplete_gamma_function#math.154.0

Formula

$K_v(x,y)=\underset{1}{\overset{\mathrm{\infty }}{\int }}\frac{e^{-xt-\frac{y}{t}}}{t^{v+1}}dt$

TeX Source

K_v(x,y)=\int_1^\infty\frac{e^{-xt-\frac{y}{t}}}{t^{v+1}}dt

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

K_v(x , y) = \int_1^\infty \frac{\expe^{-xt-\frac{y}{t}}}{t^{v+1}} \diff{t}

Expected (Gold Entry)

K_v(x , y) = \int_1^\infty \frac{\expe^{-xt-\frac{y}{t}}}{t^{v+1}} \diff{t}

Mathematica

Translation

Subscript[\[CapitalKappa], v][x , y] == Integrate[Divide[Exp[- x*t -Divide[y,t]],(t)^(v + 1)], {t, 1, Infinity}, GenerateConditions->None]

Expected (Gold Entry)

K[v_, x_, y_] := Integrate[Divide[Exp[- x*t -Divide[y,t]],(t)^(v + 1)], {t, 1, Infinity}]

Maple

Translation

Kappa[v](x , y) = int((exp(- x*t -(y)/(t)))/((t)^(v + 1)), t = 1..infinity)

Expected (Gold Entry)