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As his parents were quite poor, Raabe was forced to earn his living from a very early age by giving private lessons. He began to study mathematics in 1820 at the
Polytechnicum in
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205:{\displaystyle \int _{a}^{a+1}\log \Gamma (t)\,dt={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0.}
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