Equation 75 · Part 3 · No Particle Without a Cosigner

Symbol d

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

d

What this part means

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

Its job in the formula

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

Full expressionSymbol dArticle 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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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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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