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    You see how the Riemann zeta function is a special case of the polylogarithm, is the Dirichlet beta function a special case of any function?
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    (Original post by S.R)
    You see how the Riemann zeta function is a special case of the polylogarithm, is the Dirichlet beta function a special case of any function?
    All of them are special cases of the Lerch transcendent defined as  \Phi(z, s, \alpha) = \sum\limits_{n=0}^\infty\frac { z^n} {(n+\alpha)^s}.

    Btw, Dirichlet beta function is not 'the beta function'. That title is reserved for the truly awesome!
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    (Original post by L'art pour l'art)
    All of them are special cases of the Lerch transcendent defined as  \Phi(z, s, \alpha) = \sum\limits_{n=0}^\infty\frac { z^n} {(n+\alpha)^s}.

    Btw, Dirichlet beta function is not 'the beta function'. That title is reserved for the truly awesome!
    One function to rule them all!

    Thanks for your answer
 
 
 
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