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Problem of the Week
Evaluate the exact closed-form value of the infinite series
For any real , the generalized harmonic number is defined by
where is the digamma function and is the Euler--Mascheroni constant. Here with , all logarithms are natural logarithms, and the series is absolutely convergent.
Determine the exact value of in closed form. Your answer must be expressed as a linear combination of rational multiples of , , , and .
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