Logarithmic Functions

Functions > Symbolic Functions > Logarithmic Functions

• dilog(x)—Returns the dilogarithm function, which is defined as follows:

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    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">dilog</id>
        <id xml:space="preserve">x</id>
      </apply>
      <apply>
        <integral />
        <lambda>
          <boundVars>
            <id xml:space="preserve">τ</id>
          </boundVars>
          <apply>
            <mult />
            <apply>
              <div />
              <real>1</real>
              <apply>
                <minus />
                <real>1</real>
                <id xml:space="preserve">τ</id>
              </apply>
            </apply>
            <apply>
              <id xml:space="preserve">ln</id>
              <id xml:space="preserve">τ</id>
            </apply>
          </apply>
        </lambda>
        <lowerBound>
          <real>1</real>
        </lowerBound>
        <upperBound>
          <id xml:space="preserve">x</id>
        </upperBound>
      </apply>
    </apply>
  </math>
</region>

• polylog(n, x)—Returns the polylogarithm function, which is defined as follows:

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    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">polylog</id>
        <sequence>
          <id xml:space="preserve">n</id>
          <id xml:space="preserve">x</id>
        </sequence>
      </apply>
      <apply>
        <summation />
        <lambda>
          <boundVars>
            <id xml:space="preserve">k</id>
          </boundVars>
          <apply>
            <div />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <id xml:space="preserve">k</id>
            </apply>
            <apply>
              <pow />
              <id xml:space="preserve">k</id>
              <id xml:space="preserve">n</id>
            </apply>
          </apply>
        </lambda>
        <lowerBound>
          <real>1</real>
        </lowerBound>
        <upperBound>
          <id xml:space="preserve">∞</id>
        </upperBound>
      </apply>
    </apply>
  </math>
</region>

dilog relates to polylog as follows:

Arguments

• x is a real or complex scalar.

• n is an integer.