Leibniz formula for derivatives
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11: 14.7 Integer Degree and Order
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§14.7(ii) Rodrigues-Type Formulas
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14.7.10
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14.7.13
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14.7.14
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§14.7(iii) Reflection Formulas
…12: 18.9 Recurrence Relations and Derivatives
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§18.9(iii) Derivatives
βΊJacobi
… βΊFurther -th derivative formulas relating two different Jacobi polynomials can be obtained from §15.5(i) by substitution of (18.5.7). … βΊUltraspherical
… βΊFurther -th derivative formulas relating two different Laguerre polynomials can be obtained from §13.3(ii) by substitution of (13.6.19). …13: 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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14: 25.4 Reflection Formulas
15: 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
…16: 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
…17: 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
…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: 16.3 Derivatives and Contiguous Functions
§16.3 Derivatives and Contiguous Functions
βΊ§16.3(i) Differentiation Formulas
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16.3.1
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16.3.4
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16.3.5
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20: 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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