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Erratum to: The Power of q

  • Michael D. HirschhornEmail author
Erratum
Part of the Developments in Mathematics book series (DEVM, volume 49)

Erratum to: M.D. Hirschhorn, The Power of q, Developments in Mathematics 49, DOI  10.1007/978-3-319-57762-3

The following changes have been made to the text.

In the preface, page xiii, line 23, “than p(N)” has been corrected to “then p(N)”.

The font used in Chapter 1 for \(\phi\) and \(\psi\) has been changed to accord with the font used in later chapters.

In Chapter 1, page 12

\(\displaystyle { \left[ \begin{matrix} 0\\ 0 \end{matrix} \right] _0}\) has been corrected to \(\displaystyle { \left[ \begin{matrix} 0\\ 0 \end{matrix} \right] _q}\)

In Chapter 3, equation (3.4.2),

\(\frac{(q^3;q^3)_\infty ^3) ^2}{(q;q)_\infty ^7}\) has been corrected to \(\frac{( (q;q)_\infty ^3) ^2}{(q;q)_\infty ^7}\)

In Chapter 6, in equations (6.6.6) and (6.6.7) and the Exercise at the top of page 68, the \((-2)^{\alpha}\) has been corrected to \((-2)^{\alpha-1}\).

In Chapter 10, below the equation (10.7.6), the word “Exercise” has been moved to the next line.

In Chapter 10, page 99, “differentin” has been corrected to “different in”

In Chapter 12, page 118,

\((q^{22}, q^{33}, q^{44}, q^{55} , q^{66}, q^{77}, q^{88}, q^{88}; q^{121} )_\infty\)

has been corrected to

\((q^{22}, q^{33}, q^{44}, q^{55} , q^{66}, q^{77}, q^{88}, q^{99}; q^{121} )_\infty\)

In Chapter 17, page 161, “equivalent to (17.1.1)” has been corrected to “equivalent to (17.1.1) and (17.1.2)”

In Chapter 30, page 274,

\(=32\left( \begin{matrix} q^3,q^4,q^4,q^8,q^9,q^{12}, q^{12}, q^{12}, q^{15}, q^{16}, q^{20}, q^{20}, q^{21}, q^{24}, q^{24}, q^{24}\\ q, q^2,q^2,q^5,q^7,q^{10}, q^{10} q^{11}, q^{13}, q^{14}, q^{14}, q^{17}, q^{19}, q^{22}, q^{22}, q^{23} \end{matrix};q^{24}\right) _\infty . \)

has been corrected to

\(=32\left( \begin{matrix} q^3,q^4,q^4,q^8,q^9,q^{12}, q^{12}, q^{12}, q^{15}, q^{16}, q^{20}, q^{20}, q^{21}, q^{24}, q^{24}, q^{24}\\ q, q^2,q^2,q^5,q^7,q^{10}, q^{10},q^{11}, q^{13}, q^{14}, q^{14}, q^{17}, q^{19}, q^{22}, q^{22}, q^{23} \end{matrix};q^{24}\right) _\infty . \)

In Chapter 30, page 276, the second occurrence of the line

\(\times \left( \left( \phi (q^{12})+2q^3\psi (q^{24})\right) \psi (q^4) +q\left( \phi (q^4)+2q\psi (q^8)\right) \psi (q^{12})\right) \)

is incorrect, and has been corrected to

\(\times (\phi (q^{12})\psi (q^{4})+2q^2\psi (q^{8})\psi (q^{12}) +q(\phi (q^4)\psi (q^{12}) +2q^2\psi (q^{4})\psi (q^{24})))\)

In Chapter 34, page 313,

\(=4(q, q^{2}, q^{3}, q^{4}, q^{4} , q^{6}, q^{7}, q^{8}, q^{9}, q^{10}, q^{10}\)

has been corrected to

\(=4(q, q^{2}, q^{3}, q^{4}, q^{4} , q^{6}, q^{7}, q^{8}, q^{9}, q^{10}, q^{10},\)

In Chapter 35, equation (35.1.4), \((1+qt)^{\frac{1}{4}}\) has been corrected to \((1+qt)^{\frac{1}{2}}\).

In equation (35.1.5), \((1+2qt)^{\frac{1}{2}}\) has been corrected to \((1+2qt)^{\frac{1}{4}}\).

In Chapter 36, equation (36.2.6)

\(64\frac{\psi (q)^7}{\phi (-q^2)^8}\) has been corrected to \(64\frac{\psi (q)^7}{\phi (-q)^8}\)

In Chapter 37, equation (37.3.5)

\(\frac{abc+q^5c^3}{\phi (q^5)}\) has been corrected to \(\frac{abc+q^5c^3}{\psi (q^5)}\)

\(\frac{c(ab+q^5c^2)}{\phi (q^5)^2}\) has been corrected to \(\frac{c(ab+q^5c^2)}{\psi (q^5)}\)

In Chapter 38, page 354,

\(\frac{(q^2;q^2)_\infty ^3(q^3;q^3)_\infty ^3(q^{12};q^{12})_\infty ^3}{(q;q)_\infty (q^4;q^4)_\infty (q^6;q^6)_\infty ^8}\) in equation (38.3.2) and below equation (38.3.8) has been corrected to \(\frac{(q^2;q^2)_\infty ^3(q^3;q^3)_\infty ^3(q^{12};q^{12})_\infty ^3}{(q;q)_\infty (q^4;q^4)_\infty (q^6;q^6)_\infty ^9}\).

In Chapter 38, page 355,

\(8q\frac{(q^3;q^3)_\infty ^3(q^4;q^4)_\infty ^2(q^{12};lq^{12})_\infty ^2}{(q;q)_\infty ^7(q^2;q^2)_\infty ^3}\) has been corrected to \(8q\frac{(q^3;q^3)_\infty ^3(q^4;q^4)_\infty ^2(q^{12};q^{12})_\infty ^2}{(q;q)_\infty ^7(q^2;q^2)_\infty ^3}\).

In Chapter 38, page 356

\(2q\frac{(q^2;q^2)_\infty ^5(q^{12};q^{12})_\infty ^6}{(q^4;q^4)_\infty ^2(q^6;q^6)_\infty ^9}\) has been corrected to \(2q\frac{(q^2;q^2)_\infty ^3(q^{12};q^{12})_\infty ^6}{(q^4;q^4)_\infty ^2(q^6;q^6)_\infty ^9}\).

The book has been updated with the changes.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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