- Page 1: Solving Differential Equations in T
- Page 5 and 6: List of Notations This is a list of
- Page 7 and 8: Introduction Ordinary differential
- Page 9 and 10: 1 Preliminaries We will first intro
- Page 11 and 12: 1.2. SINGULAR POINTS 11 A linear di
- Page 13 and 14: 1.3. HYPERGEOMETRIC SERIES 13 Theor
- Page 15 and 16: 1.3. HYPERGEOMETRIC SERIES 15 1.3.1
- Page 17 and 18: 1.3. HYPERGEOMETRIC SERIES 17 Remar
- Page 19 and 20: 1.4. FORMAL SOLUTIONS AND GENERALIZ
- Page 21 and 22: 1.4. FORMAL SOLUTIONS AND GENERALIZ
- Page 23 and 24: 1.4. FORMAL SOLUTIONS AND GENERALIZ
- Page 25 and 26: 1.4. FORMAL SOLUTIONS AND GENERALIZ
- Page 27 and 28: 2 Transformations From now on we wi
- Page 29 and 30: 2.1. OPERATORS OF DEGREE TWO 29 in
- Page 31 and 32: 2.1. OPERATORS OF DEGREE TWO 31 r 3
- Page 33 and 34: 2.1. OPERATORS OF DEGREE TWO 33 The
- Page 35 and 36: 2.1. OPERATORS OF DEGREE TWO 35 The
- Page 37 and 38: 2.2. THE EXPONENT DIFFERENCE 37 > g
- Page 39 and 40: 2.2. THE EXPONENT DIFFERENCE 39 whe
- Page 41 and 42: 2.3. EQUIVALENCE OF DIFFERENTIAL OP
- Page 43 and 44: 2.3. EQUIVALENCE OF DIFFERENTIAL OP
- Page 45 and 46: 2.3. EQUIVALENCE OF DIFFERENTIAL OP
- Page 47 and 48: 3 Solving in Terms of Bessel Functi
- Page 49 and 50: 3.1. CHANGE OF VARIABLES 49 We star
- Page 51 and 52: 3.1. CHANGE OF VARIABLES 51 ⇒ ∆
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3.2. FINDING THE PARAMETER ν 53 Ex
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3.2. FINDING THE PARAMETER ν 55 If
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3.3. THE ALGORITHM 57 3.3 The Algor
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3.3. THE ALGORITHM 59 Example 3.12
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3.3. THE ALGORITHM 61 > gen exp(L,t
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3.3. THE ALGORITHM 63 We can also f
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3.3. THE ALGORITHM 65 > equiv(L,M);
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3.3. THE ALGORITHM 67 must be a mul
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3.3. THE ALGORITHM 69 2. Let ai,bi
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3.3. THE ALGORITHM 71 The exp-regul
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3.4. SOLVING OVER A GENERAL FIELD K
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3.4. SOLVING OVER A GENERAL FIELD K
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3.4. SOLVING OVER A GENERAL FIELD K
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3.4. SOLVING OVER A GENERAL FIELD K
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3.5. WHITTAKER FUNCTIONS 81 At x =
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3.6. TWO FINAL EXAMPLES 83 > LW:=D
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3.6. TWO FINAL EXAMPLES 85 Since Wh
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4 Conclusion We developed an algori
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A Appendix A.1 Transformations From
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A.3. PACKAGE DESCRIPTION 91 coeffic
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A.3. PACKAGE DESCRIPTION 93 findWhi
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Bibliography [1] ABRAMOV, S. A., BA
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BIBLIOGRAPHY 97 [23] VAN HOEIJ, M.
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Index adjoint operator, 42, 44 alge