multivalued function
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31: 7.18 Repeated Integrals of the Complementary Error Function
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►The confluent hypergeometric function on the right-hand side of (7.18.10) is multivalued and in the sectors one has to use the analytic continuation formula (13.2.12).
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32: 12.7 Relations to Other Functions
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►(It should be observed that the functions on the right-hand sides of (12.7.14) are multivalued; hence, for example, cannot be replaced simply by .)
33: 19.18 Derivatives and Differential Equations
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§19.18(i) Derivatives
… ►§19.18(ii) Differential Equations
… ►The function satisfies an Euler–Poisson–Darboux equation: …Also , with , satisfies a wave equation: …Similarly, the function satisfies an equation of axially symmetric potential theory: …34: 19.2 Definitions
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►Let be a cubic or quartic polynomial in with simple zeros, and let be a rational function of and containing at least one odd power of .
…where is a polynomial in while and are rational functions of .
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§19.2(iv) A Related Function:
… ►In (19.2.18)–(19.2.22) the inverse trigonometric and hyperbolic functions assume their principal values (§§4.23(ii) and 4.37(ii)). When and are positive, is an inverse circular function if and an inverse hyperbolic function (or logarithm) if : …35: 19.20 Special Cases
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►In this subsection, and also §§19.20(ii)–19.20(v), the variables of all -functions satisfy the constraints specified in §19.16(i) unless other conditions are stated.
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19.20.5
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►When the variables are real and distinct, the various cases of are called circular (hyperbolic) cases if is positive (negative), because they typically occur in conjunction with inverse circular (hyperbolic) functions.
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19.20.19
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19.20.25
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