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Observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>500</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo…
Using a data sample corresponding to an integrated luminosity of 2.93 fb^{-1} recorded by the BESIII detector at a center-of-mass energy of 3.773 GeV, we present an analysis of the decays D^{0}→π^{-}π^{0}e^{+}ν_{e} and D^{+}→π^{-}π^{+}e^{+}ν_{e}. By performing a partial wave analysis, the π^{+}π^{-} S-wave contribution to D^{+}→π^{-}π^{+}e^{+}ν_{e} is observed to be …