program define pdf_t
    version 4.0

    local x = "`1'"
    local fx =  "`2'"
    local df = `3'

    quietly {
        local c1 = lngamma((`df'/2)+.5)-lngamma(.5)-lngamma(`df'/2)-.5*log(`df')
        local c2 = (`df'+1)/2
        replace `fx' = exp(`c1'-`c2'*log(1+(`x'^2)/`df'))
    }

end