Leibniz formula for derivatives
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11: 15.5 Derivatives and Contiguous Functions
§15.5 Derivatives and Contiguous Functions
βΊ§15.5(i) Differentiation Formulas
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15.5.2
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15.5.10
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12: 25.4 Reflection Formulas
13: 4.38 Inverse Hyperbolic Functions: Further Properties
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§4.38(ii) Derivatives
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4.38.9
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4.38.11
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4.38.13
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§4.38(iii) Addition Formulas
…14: 10.49 Explicit Formulas
§10.49 Explicit Formulas
βΊ§10.49(i) Unmodified Functions
… βΊ§10.49(ii) Modified Functions
… βΊ§10.49(iii) Rayleigh’s Formulas
… βΊ§10.49(iv) Sums or Differences of Squares
…15: 1.8 Fourier Series
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βΊat every point at which has both a left-hand derivative (that is, (1.4.4) applies when ) and a right-hand derivative (that is, (1.4.4) applies when ).
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Parseval’s Formula
… βΊPoisson’s Summation Formula
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1.8.16
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16: 10.61 Definitions and Basic Properties
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10.61.3
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10.61.4
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§10.61(iii) Reflection Formulas for Arguments
… βΊ§10.61(iv) Reflection Formulas for Orders
…17: 18.9 Recurrence Relations and Derivatives
18: 25.18 Methods of Computation
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§25.18(i) Function Values and Derivatives
βΊThe principal tools for computing are the expansion (25.2.9) for general values of , and the Riemann–Siegel formula (25.10.3) (extended to higher terms) for . …Calculations relating to derivatives of and/or can be found in Apostol (1985a), Choudhury (1995), Miller and Adamchik (1998), and Yeremin et al. (1988). …19: 3.5 Quadrature
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βΊIf in (3.5.4) is not arbitrarily large, and if odd-order derivatives of are known at the end points and , then the composite trapezoidal rule can be improved by means of the Euler–Maclaurin formula (§2.10(i)).
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