{ "definitions": { "y": [ { "Q12916": "real number", "Q50701": "variable" } ] }, "constraints": [], "math_inputtex": "\\[\\Im\\psi\\left(\\tfrac{1}{2}+iy\\right)=\\frac{\\pi}{2}\\tanh\\left(\\pi y\\right),\\]", "math_inputtex_semantic": "\\wf{Q11348}{\\Im}\\wf{Q905326}{\\digamma} (\\tfrac{1}{2} + \\iunit \\w{Q12916}{y}) = \\frac{\\cpi}{2} \\tanh@{\\cpi y}", "correct_tex": "\\Im\\psi\\left(\\tfrac{1}{2}+iy\\right)=\\frac{\\pi}{2}\\tanh\\left(\\pi y\\right)", "correct_mml": "\n \n \n \n ℑ\n ⁢\n \n ϝ\n ⁡\n \n (\n \n \n 1\n 2\n \n +\n \n i\n ⁢\n y\n \n \n )\n \n \n \n =\n \n \n π\n 2\n \n ⁢\n \n tanh\n ⁡\n \n (\n \n π\n ⁢\n y\n \n )\n \n \n \n \n \n \n \n \n \n Q11348\n \n Q905326\n \n \n \n \n 1\n 2\n \n \n \n imaginary-unit\n 𝑦\n \n \n \n \n \n \n \n \n \n 2\n \n \n \n \n \n \n 𝑦\n \n \n \n \n \n \\Im\\digamma(\\tfrac{1}{2}+\\mathrm{i}y)=\\frac{\\pi}{2}\\tanh\\left(\\pi y\\right)\n \n\n", "uri": "http://dlmf.nist.gov/5.4#E17", "title": "DLMF:_5.4_Special_Values_and_Extrema", "type": "equation", "check": { "tree": true, "qid": false }, "substitutions": {} }