"November 2007, volume 190, number 888 (first of three numbers)."

Includes bibliographical references (p. 357-358) and index.

Part 1. Foundations for a general theory 1. Introduction 2. The coefficients $c^*_{i,j}(z)$ of (1.3) 3. The coefficients $c^{**}_{i,j}(\zeta )$ of (1.5) 4. Isolated results needed for completeness 5. Composite transformations and reductions 6. Related Laguerre-Forsyth canonical forms Part 2. The basic relative invariants for $Q_m=0$ when $m\ge 2$ 7. Formulas that involve $L_{i,j}(z)$ 8. Basic semi-invariants of the first kind for $m \geq 2$ 9. Formulas that involve $V_{i,j}(z)$ 10. Basic semi-invariants of the second kind for $m \geq 2$ 11. The existence of basic relative invariants 12. The uniqueness of basic relative invariants 13. Real-valued functions of a real variable Part 3. Supplementary results 14. Relative invariants via basic ones for $m \geq 2$ 15. Results about $Q_m$ as a quadratic form 16. Machine computations 17. The simplest of the Fano-type problems for (1.1) 18. Paul Appell's condition of solvability for $Q_m = 0$ 19. Appell's condition for $Q_2 = 0$ and related topics 20. Rational semi-invariants and relative invariants Part 4. Generalizations for $H_{m,n}=0$ 21. Introduction to the equations $H_{m,n} = 0$ 22. Basic relative invariants for $H_{1,n} = 0$ when $n \geq 2$ 23. Laguerre-Forsyth forms for $H_{m,n} = 0$ when $m \geq 2$ 24. Formulas for basic relative invariants when $m \geq 2$ 25. Extensions of Chapter 7 to $H_{m,n} = 0$, when $m \geq 2$ 26. Extensions of Chapter 9 to $H_{m,n} = 0$, when $m \geq 2$ 27. Basic relative invariants for $H_{m,n} = 0$ when $m \geq 2$ Part 5. Additional classes of equations 28. The class of equations specified by $y"(z) y'(z)$ 29. Formulations of greater generality 30. Invariants for simple equations unlike (29.1)

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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