Equation 75 · Part 1 · No Particle Without a Cosigner

Symbol x

\int_0^\infty x(e^x-1)^{-1}dx=\pi^2/6

x

What this part means

x is part of the quantity the equation computes from the expression on the right.

Its job in the formula

x is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol xArticle meaning

The passage around this formula

Write the normalized accelerated spectrum in terms of the dimensionless ratio u $\equiv$ c $\Omega$ /a , using the exact Bose-Einstein shape derived above. Carrying out the normalization integral, $\int_0^\infty$ $\Omega$ \,( $e^{2\pi c\Omega/a}$ -1)^{-1}\,d $\Omega$ = $a^2$ /(24 $c^2$ ) , using the standard result $\int_0^\infty$ x( $e^x$ -1)^{-1}dx= $\pi^2$ /6 , gives the scale-family form

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

[9] Asymptotic States of Accelerated Detectors and Universality of the Unruh Effect ↗

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