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1: 4.13 Lambert -Function
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►We call the increasing solution for which the principal branch and denote it by .
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►Other solutions of (4.13.1) are other branches of .
…The other branches
are single-valued analytic functions on , have a logarithmic branch point at , and, in the case , have a square root branch point at respectively.
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2: 4.24 Inverse Trigonometric Functions: Further Properties
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3: 1.10 Functions of a Complex Variable
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►If and , then one branch is , the other branch is , with in both cases.
Similarly if , then one branch is , the other branch is , with in both cases.
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►(b) By specifying the value of at a point (not a branch point), and requiring to be continuous on any path that begins at and does not pass through any branch points or other singularities of .
►If the path circles a branch point at , times in the positive sense, and returns to without encircling any other branch point, then its value is denoted conventionally as .
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4: 15.2 Definitions and Analytical Properties
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►again with analytic continuation for other values of , and with the principal branch defined in a similar way.
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►The same is true of other branches, provided that , , and are excluded.
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5: 4.37 Inverse Hyperbolic Functions
6: 10.21 Zeros
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►For further information, including uniform asymptotic expansions, extensions to other branches of the functions and their derivatives, and extensions to half-integer values of the order, see Olver (1954).
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7: 31.11 Expansions in Series of Hypergeometric Functions
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►The expansion (31.11.1) for a Heun function that is associated with any branch of (31.11.2)—other than a multiple of the right-hand side of (31.11.12)—is convergent inside the ellipse .
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