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DivisorSigma






Mathematica Notation

Traditional Notation









Number Theory Functions > DivisorSigma[k,n] > Summation > Finite summation





http://functions.wolfram.com/13.05.23.0003.01









  


  










Input Form





Sum[DivisorSigma[r, k] DivisorSigma[s, n - k], {k, 1, n - 1}] == (DivisorSigma[r + s + 1, n] Gamma[r + 1] Gamma[s + 1] Zeta[r + 1] Zeta[s + 1])/(Gamma[r + s + 2] Zeta[r + s + 2]) + (n DivisorSigma[r + s - 1, n] (Zeta[1 - r] + Zeta[1 - s]))/(r + s) - (1/2) DivisorSigma[s, n] Zeta[-r] - (1/2) DivisorSigma[r, n] Zeta[-s] /; (r == 1 && s == 3) || (r == 1 && s == 5) || (r == 1 && s == 7) || (r == 1 && s == 11) || (r == 3 && s == 3) || (r == 3 && s == 5) || (r == 3 && s == 9) || (r == 5 && s == 7)










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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