stable pairs
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11: 8.25 Methods of Computation
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►Stable recursive schemes for the computation of are described in Miller (1960) for and integer .
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12: 32.4 Isomonodromy Problems
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– can be expressed as the compatibility condition of a linear system, called an isomonodromy problem or Lax pair.
Suppose
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13: 10.25 Definitions
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§10.25(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1). … ►14: 27.5 Inversion Formulas
15: 27.15 Chinese Remainder Theorem
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►The Chinese remainder theorem states that a system of congruences , always has a solution if the moduli are relatively prime in pairs; the solution is unique (mod ), where is the product of the moduli.
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16: 27.19 Methods of Computation: Factorization
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►Type II probabilistic algorithms for factoring rely on finding a pseudo-random pair of integers that satisfy .
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17: 9.17 Methods of Computation
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►In the case of the Scorer functions, integration of the differential equation (9.12.1) is more difficult than (9.2.1), because in some regions stable directions of integration do not exist.
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18: 11.13 Methods of Computation
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►Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that and can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity.
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19: 9.2 Differential Equation
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