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11: 10.39 Relations to Other Functions

§10.39 Relations to Other Functions

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Elementary Functions

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Parabolic Cylinder Functions

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Confluent Hypergeometric Functions

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Generalized Hypergeometric Functions and Hypergeometric Function

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12: 20.9 Relations to Other Functions

§20.9 Relations to Other Functions

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§20.9(i) Elliptic Integrals

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§20.9(ii) Elliptic Functions and Modular Functions

… ►The relations (20.9.1) and (20.9.2) between $k$ and $\tau$ (or $q$) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). … ►

§20.9(iii) Riemann Zeta Function

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13: 31.7 Relations to Other Functions

§31.7 Relations to Other Functions

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§31.7(i) Reductions to the Gauss Hypergeometric Function

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§31.7(ii) Relations to Lamé Functions

… ►Similar specializations of formulas in §31.3(ii) yield solutions in the neighborhoods of the singularities $\zeta =K$, $K+\mathrm{i}{K}^{\prime }$, and $\mathrm{i}{K}^{\prime }$, where $K$ and $K^{\prime }$ are related to $k$ as in §19.2(ii).

14: 10.16 Relations to Other Functions

§10.16 Relations to Other Functions

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Elementary Functions

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Parabolic Cylinder Functions

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Confluent Hypergeometric Functions

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Generalized Hypergeometric Functions

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15: 7.5 Interrelations

§7.5 Interrelations

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16: 6.5 Further Interrelations

§6.5 Further Interrelations

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17: 15.9 Relations to Other Functions

§15.9 Relations to Other Functions

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§15.9(i) Orthogonal Polynomials

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Jacobi

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Legendre

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Meixner

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18: 7.18 Repeated Integrals of the Complementary Error Function

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§7.18(iv) Relations to Other Functions

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Hermite Polynomials

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Confluent Hypergeometric Functions

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Parabolic Cylinder Functions

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Probability Functions

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19: 16.18 Special Cases

§16.18 Special Cases

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20: 4.28 Definitions and Periodicity

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Relations to Trigonometric Functions

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