On an integral in the theory of signal detection (Q1357928)
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scientific article; zbMATH DE number 1023841
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an integral in the theory of signal detection |
scientific article; zbMATH DE number 1023841 |
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On an integral in the theory of signal detection (English)
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27 July 1997
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E. R. Love considered the integral \(I_2=\int^\infty_0(\arcsin e^{-t})^2dt\) playing a certain role in the theory of signal detection and obtained the bounds \(0.6552<I_2<0.6609\). In the present article we establish the exact equality \(I_2=({\pi\over 2})^2\ln 2-\lambda(3)\), where \(\lambda(n)=\sum^\infty_{i=0}(2i+1)^{-n}\).
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signal detection
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0.6519131064414978
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0.6489886045455933
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0.6489439010620117
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