<p>We prove a Lie–Trotter type formula for <i>q</i>-exponential operators: <Equation ID="Equ5"> <EquationSource Format="TEX">\(\begin{aligned} \lim \limits _{n\rightarrow \infty }\left[ \left( I+\left( 1-q\right) \frac{U}{ n}\right) ^{\frac{1}{1-q}}\left( I+\left( 1-q\right) \frac{V}{n}\right) ^{ \frac{1}{1-q}}\right] ^{n}=e^{U+V} \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <munder> <mo movablelimits="false">lim</mo> <mrow> <mi>n</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </munder> <msup> <mfenced close="]" open="["> <msup> <mfenced close=")" open="("> <mi>I</mi> <mo>+</mo> <mfenced close=")" open="("> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mfenced> <mfrac> <mi>U</mi> <mi>n</mi> </mfrac> </mfenced> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mrow> </mfrac> </msup> <msup> <mfenced close=")" open="("> <mi>I</mi> <mo>+</mo> <mfenced close=")" open="("> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mfenced> <mfrac> <mi>V</mi> <mi>n</mi> </mfrac> </mfenced> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mrow> </mfrac> </msup> </mfenced> <mi>n</mi> </msup> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mi>U</mi> <mo>+</mo> <mi>V</mi> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>where <i>E</i> is a Banach space, <i>U</i>,&#xa0;<i>V</i> bounded linear operators on <i>E</i> and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q\in \mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>∈</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q\ne 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≠</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>