values at z=0
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1—10 of 143 matching pages
1: 20.4 Values at = 0
2: 12.2 Differential Equations
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§12.2(ii) Values at
…3: 18.6 Symmetry, Special Values, and Limits to Monomials
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Laguerre
…4: 12.14 The Function
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§12.14(ii) Values at and Wronskian
…5: 6.4 Analytic Continuation
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►Analytic continuation of the principal value of yields a multi-valued function with branch points at
and .
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6: 4.2 Definitions
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►This is a multivalued function of with branch point at
.
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7: 31.3 Basic Solutions
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denotes the solution of (31.2.1) that corresponds to the exponent
at
and assumes the value
there.
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8: 10.25 Definitions
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►In particular, the principal branch of is defined in a similar way: it corresponds to the principal value of , is analytic in , and two-valued and discontinuous on the cut .
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►It has a branch point at
for all .
The principal branch corresponds to the principal value of the square root in (10.25.3), is analytic in , and two-valued and discontinuous on the cut .
►Both and are real when is real and .
►For fixed
each branch of and is entire in .
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9: 10.2 Definitions
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►This differential equation has a regular singularity at
with indices , and an irregular singularity at
of rank ; compare §§2.7(i) and 2.7(ii).
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►This solution of (10.2.1) is an analytic function of , except for a branch point at
when is not an integer.
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►Whether or not is an integer has a branch point at
.
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►Each solution has a branch point at
for all .
The principal branches correspond to principal values of the square roots in (10.2.5) and (10.2.6), again with a cut in the -plane along the interval .
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