{ "definitions" : { "f" : [ { "Q319913" : "convex function" } ], "x" : [ { "Q12916" : "real number (quantity along a continuous line)" } ], "y" : [ { "Q12916" : "real number (quantity along a continuous line)" } ], "p" : [ { "Q2627460" : "Conjugate variables" } ], "v" : [ { "Q2627460" : "Conjugate variables" } ] }, "constraints" : [ ], "math_inputtex" : "df = {\\partial f \\over \\partial x}dx + {\\partial f \\over \\partial y}dy = pdx + vdy", "math_inputtex_semantic" : "d \\w{Q319913}{f} = {\\partial f \\over \\partial \\w{Q12916}{x}}dx + {\\partial f \\over \\partial \\w{Q12916}{y}}dy = \\w{Q2627460}{p} dx + \\w{Q2627460}{v} dy", "correct_tex" : "df = {\\partial f \\over \\partial x}dx + {\\partial f \\over \\partial y}dy = p dx + v dy", "correct_mml" : "\n \n \n \n d\n ⁢\n f\n \n =\n \n \n \n \n ∂\n ⁡\n f\n \n \n ∂\n ⁡\n x\n \n \n ⁢\n d\n ⁢\n x\n \n +\n \n \n \n ∂\n ⁡\n f\n \n \n ∂\n ⁡\n y\n \n \n ⁢\n d\n ⁢\n y\n \n \n =\n \n \n p\n ⁢\n d\n ⁢\n x\n \n +\n \n v\n ⁢\n d\n ⁢\n y\n \n \n \n \n \n \n \n \n \n \n 𝑑\n Q319913\n \n \n \n \n \n \n \n \n \n Q319913\n \n \n \n Q12916\n \n \n 𝑑\n Q12916\n \n \n \n \n \n \n \n Q319913\n \n \n \n Q12916\n \n \n 𝑑\n Q12916\n \n \n \n \n \n \n \n \n \n \n Q2627460\n 𝑑\n Q12916\n \n \n \n Q2627460\n 𝑑\n Q12916\n \n \n \n \n \n df={\\partial f\\over\\partial x}dx+{\\partial f\\over\\partial y}dy=pdx+vdy\n \n", "uri" : "https://en.formulasearchengine.com/w/index.php?oldid=4480#math4480.29", "title" : "Legendre_transformation", "type" : "definition" }