Application of the uniformized Mittag-Leffler expansion to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">?</mml:mi><mml:mo>(</mml:mo><mml:mn>1405</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>

We study the pole properties of $\Lambda(1405)$ in a model-independent manner by applying Uniformized Mittag-Leffler expansion proposed our previous paper. The resonant energy, width and residues are determined expanding observable as sum resonant-pole pairs under an appropriate parameterization which expresses to be single-valued, fitting it experimental data invariant-mass distribution $\pi^+\Sigma^-$, $\pi^-\Sigma^+$, $\pi^0\Sigma^0$ final states reaction, $\gamma p \rightarrow K^+ \pi \Sigma$, elastic inelastic cross section, $K^-p\to K^-p$, $\bar{K}^0n$, $\pi^-\Sigma^+$. As we gradually increase number from one three, first pair converges while second third emerge further away pair, implying that with three is almost convergent vicinity $\Lambda(1405)$. broad peak structure between $\pi\Sigma$ $\bar{K} N$ thresholds regarded explained single energy 1420 $\pm$ 1 MeV, half 48 2 consistent single-pole picture conclude turns out very powerful method obtain resonance near-threshold spectrum.