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Watson's Identities

Watson's identities evaluate combinations of the Rogers L-function at roots of a cubic equation. Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation

t^3+2t^2-t-1=0,
(1)

then the Rogers L-function satisfies

L(alpha)-L(alpha^2)=1/7
(2)
L(beta)+1/2L(beta^2)=5/7
(3)
L(gamma)+1/2L(gamma^2)=4/7.
(4)

See also

L-Algebraic Number, Rogers L-Function, Watson's Formula, Watson's Triple Integrals

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References

Bytsko, A. G. "Two-Term Dilogarithm Identities Related to Conformal Field Theory." 9 Nov 1999. https://arxiv.org/abs/math-ph/9911012.Watson, G. N. "A Note on Spence's Logarithmic Transcendent." Quart. J. Math. Oxford Ser. 8, 39-42, 1937.

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Watson's Identities

Cite this as:

Weisstein, Eric W. "Watson's Identities." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WatsonsIdentities.html

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