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11: 10.34 Analytic Continuation
12: 26.10 Integer Partitions: Other Restrictions
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►The set is denoted by .
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►where the last right-hand side is the sum over
of the generating functions for partitions into distinct parts with largest part equal to .
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►where the sum is over nonnegative integer values of for which .
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►where the sum is over nonnegative integer values of for which .
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►where the sum is over nonnegative integer values of for which .
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13: 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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10.2.4
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►The principal branch corresponds to the principal branches of in (10.2.3) and (10.2.4), with a cut in the -plane along the interval .
►Except in the case of , the principal branches of and are two-valued and discontinuous on the cut ; compare §4.2(i).
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►The principal branches of and are two-valued and discontinuous on the cut .
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14: 3.5 Quadrature
15: 10.36 Other Differential Equations
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10.36.2
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16: 10.43 Integrals
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§10.43(ii) Integrals over the Intervals and
… ►§10.43(iv) Integrals over the Interval ()
… ► …17: 4.4 Special Values and Limits
18: 33.2 Definitions and Basic Properties
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§33.2(ii) Regular Solution
… ►§33.2(iii) Irregular Solutions
►The functions are defined by … ►As in the case of , the solutions and are analytic functions of when . Also, are analytic functions of when . …19: 22.19 Physical Applications
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►The periodicity and symmetry of the pendulum imply that the motion in each four intervals and have the same “quarter periods” .
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►As from below the period diverges since are points of unstable equilibrium.
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►For an initial displacement with , bounded oscillations take place near one of the two points of stable equilibrium .
…For initial displacement with the motion extends over the full range :
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