What is recorded here?
Euler evaluated the sum of reciprocal squares of the positive integers as π²/6. His E41 paper developed connections between even reciprocal-power series and trigonometric expansions. A simple arithmetic series had resisted an exact expression. Euler related its sum to the circle constant through trigonometric expansions and their roots. The surviving paper identifies a specific analytic result and historical derivation, independently of the bridges problem.
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Scientific scope
This is a historical evaluation without an independent WRS proof audit. The paper's infinite factor reasoning is its original derivation; no claim is made that odd reciprocal-power sums were all evaluated.
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People and systems
Leonhard Euler
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English catalogue narrative
Euler: the reciprocal-square sum and the circle constant
Euler evaluated the sum of reciprocal squares of the positive integers as π²/6. His E41 paper developed connections between even reciprocal-power series and trigonometric expansions.
A simple arithmetic series had resisted an exact expression. Euler related its sum to the circle constant through trigonometric expansions and their roots. The surviving paper identifies a specific analytic result and historical derivation, independently of the bridges problem.
Scientific scope
This is a historical evaluation without an independent WRS proof audit. The paper's infinite factor reasoning is its original derivation; no claim is made that odd reciprocal-power sums were all evaluated.
People and systems
Leonhard Euler