differentiation formulas

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1: 27.20 Methods of Computation: Other Number-Theoretic Functions

… ►A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function $\tau \left(n\right)$, and the values can be checked by the congruence (27.14.20). …

2: 16.3 Derivatives and Contiguous Functions

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§16.3(i) Differentiation Formulas

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3: 13.3 Recurrence Relations and Derivatives

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§13.3(ii) Differentiation Formulas

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4: 15.5 Derivatives and Contiguous Functions

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§15.5(i) Differentiation Formulas

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5: 18.9 Recurrence Relations and Derivatives

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§18.9(iii) Derivatives

… ►See also the differentiation formulas in (Erdélyi et al., 1953b, §10.9(15))). …

6: 18.3 Definitions

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With the property that ${\{p_{n+1}^{\prime }(x)\}}_{n=0}^{\mathrm{\infty }}$ is again a system of OP’s. See §18.9(iii).

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7: 5.19 Mathematical Applications

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8: 13.15 Recurrence Relations and Derivatives

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§13.15(ii) Differentiation Formulas

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9: 18.2 General Orthogonal Polynomials

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Degree lowering and raising differentiation formulas and structure relations

►For a large class of OP’s $p_n$ there exist pairs of differentiation formulas …

10: 13.10 Integrals

… ►Other formulas of this kind can be constructed by inversion of the differentiation formulas given in §13.3(ii). …