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Abstract In this study, we give a kind of sharp Wirtinger inequality ∥f∥p≤Cr,p,q∥f(r)∥qfor all 1≤p,q≤∞, $$ \Vert f \Vert _{p}\le C_{r,p,q} \bigl\Vert f^{(r)} \bigr\Vert _{q} \quad \text{for all } 1\le p,q\le \infty , $$ where f is defined on [0,1] $[0,1]$ and satisfies f(k1)(0)=f(k2)(0)=⋯=f(ks)(0)=f(ms+1)(1)=⋯=f(mr)(1)=0 $f^{(k_{1})}(0)=f^{(k _{2})}(0)=\cdots =f^{(k_{s})}(0)=f^{(m_{s+1})}(1)=\cdots =f^{(m_{r})}(1)=0$ with 0≤k1<k2<⋯<ks≤r−1 $0\le k_{1}< k_{2}<\cdots <k_{s}\le r-1$ and 0≤ms+1<ms+2<⋯<mr≤r−1 $0\le m_{s+1}< m_{s+2}< \cdots <m_{r}\le r-1$. First, based on the Birkhoff interpolation, we refer the computation of Cr,p,q $C_{r,p,q}$ to the norm of an integral-type operator. Second, we refer the values of Cr,1,1 $C_{r,1,1}$ and Cr,∞,∞ $C_{r,\infty ,\infty }$ to explicit integral expressions and the value of Cr,2,2 $C_{r,2,2}$ to the computation of the maximal eigenvalue of a Hilbert–Schmidt operator. Finally, we give three examples to show our method.