continuously%20differentiable
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11: 1.6 Vectors and Vector-Valued Functions
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โบwhen is continuously differentiable.
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โบFor , , and
continuously differentiable, the vectors
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โบwhen is a continuously differentiable vector-valued function.
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โบwhen is a continuously differentiable vector-valued function.
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โบFor and twice-continuously differentiable functions
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12: 3.10 Continued Fractions
§3.10 Continued Fractions
… โบA continued fraction of the form … โบA continued fraction of the form … โบ§3.10(iii) Numerical Evaluation of Continued Fractions
… โบThe continued fraction …13: 13.5 Continued Fractions
§13.5 Continued Fractions
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13.5.1
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โบThis continued fraction converges to the meromorphic function of on the left-hand side everywhere in .
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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โบThis continued fraction converges to the meromorphic function of on the left-hand side throughout the sector .
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14: 13.17 Continued Fractions
§13.17 Continued Fractions
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13.17.1
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โบThis continued fraction converges to the meromorphic function of on the left-hand side for all .
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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โบThis continued fraction converges to the meromorphic function of on the left-hand side throughout the sector .
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15: 5.10 Continued Fractions
§5.10 Continued Fractions
…16: 18.32 OP’s with Respect to Freud Weights
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โบwhere is real, even, nonnegative, and continuously differentiable, where increases for , and as , see Freud (1969).
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17: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Singularities of Differentiable Maps. Vol. II.
Birkhäuser, Boston-Berlin.
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Recurrence relations, continued fractions, and orthogonal polynomials.
Mem. Amer. Math. Soc. 49 (300), pp. iv+108.
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18: Bibliography W
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Infinitely differentiable generalized logarithmic and exponential functions.
Math. Comp. 57 (196), pp. 723–733.
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Analytic Theory of Continued Fractions.
D. Van Nostrand Company, Inc., New York.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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19: 4.39 Continued Fractions
§4.39 Continued Fractions
… โบFor these and other continued fractions involving inverse hyperbolic functions see Lorentzen and Waadeland (1992, pp. 569–571). …20: 1.5 Calculus of Two or More Variables
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โบThe function is continuously differentiable if , , and are continuous, and
twice-continuously differentiable if also , , , and are continuous.
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1.5.6
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โบIf is continuously differentiable, , and at , then in a neighborhood of , that is, an open disk centered at , the equation defines a continuously differentiable function such that , , and .
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โบIf is times continuously differentiable, then
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โบSufficient conditions for validity are: (a) and are continuous on a rectangle , ; (b) when both and are continuously differentiable and lie in .
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