# PyMieScatt > LowFrequencyMieQ() > Equation of g

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### Equation of Qsca

The implementation of g can be written as follows:

g = \frac{4}{Q_{sca}x^2}\sum(\frac{n(n+2)}{n+1}(using a_n, b_n, g1[0:4]) + \frac{2n+1}{n(n+1)}\{Re(a_n)*Re(b_n)+Im(a_n)*Im(b_n)\}


An equation similar to the above can be found:
Bohren and Huffman(1983)
p120

Q_{sca}<cos\theta> = \frac{4}{x^2}[\sum_n (\frac{n(n+2)}{n+1}Re\{a_n a_{n+1}^* + b_n b_{n+1}^* \} + \sum_n \frac{2n+1}{n(n+1)}Re\{a_n b_n^*\} ]


Since, $g = < cos\theta >$, the coefficients are same.

However, the contents of the summation seems different.

#### 1st summation

Re(a_n a_{n+1}^* + b_n b_{n+1}^*) ... (1)

a_n a_{n+1}^*

= (Re\{a_n\} + iIm\{a_n\})(Re\{a_{n+1}\} - iIm\{ a_{n+1}\})

= Re\{a_{n}\}Re\{a_{n+1}\} - - Im\{a_{n}\}Im\{a_{n+1}\}

= Re\{a_{n}\}Re\{a_{n+1}\} + Im\{a_{n}\}Im\{a_{n+1}\} ... (2)


Eq.(1) becomes using Eq.(2)

Re(a_n a_{n+1}^* + b_n b_{n+1}^*)

= Re\{a_{n}\}Re\{a_{n+1}\} + Im\{a_{n}\}Im\{a_{n+1}\}

+ Re\{b_{n}\}Re\{b_{n+1}\} + Im\{b_{n}\}Im\{b_{n+1}\}


From above, the 1st summation is same.

#### 2nd summation

a_n = Re\{a_n\} + i Im\{a_n\} ... (3)

b_n = Re\{a_n\} + i Im\{b_n\} ... (4)

a_n b_n^* = (Re\{a_n\} + i Im\{a_n\})(Re\{b_n\} - i Im\{b_n\})

= Re\{a_n\} Re\{b_n\} - - Im\{a_n\} Im\{b_n\}

Re\{ a_n b_n^* \} = Re\{a_n\} Re\{b_n\} + Im\{a_n\} Im\{b_n\}


From above, the second summation is same.