Euler%E2%80%93Maclaurin
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21: 30.5 Functions of the Second Kind
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►Other solutions of (30.2.1) with , , and are
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30.5.1
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30.5.2
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30.5.4
►with as in (30.11.4).
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22: 24.4 Basic Properties
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§24.4(i) Difference Equations
… ►§24.4(ii) Symmetry
… ►§24.4(iii) Sums of Powers
… ►§24.4(iv) Finite Expansions
… ►Next, …23: 16.16 Transformations of Variables
24: 5.13 Integrals
25: 32.8 Rational Solutions
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►In the general case assume , so that as in §32.2(ii) we may set and .
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(a)
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(c)
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(d)
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(e)
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and , where , is odd, and when .
, , and , with even.
, , and , with even.
, , and .
26: 5.22 Tables
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►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S.
Zhang and Jin (1996, pp. 67–69 and 72) tabulates , , , , , , , and for to 8D or 8S; for to 51S.
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►Abramov (1960) tabulates for () , () to 6D.
Abramowitz and Stegun (1964, Chapter 6) tabulates for () , () to 12D.
…Zhang and Jin (1996, pp. 70, 71, and 73) tabulates the real and imaginary parts of , , and for , to 8S.
27: 18.17 Integrals
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18.17.14
, .
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►For the beta function see §5.12, and for the confluent hypergeometric function see (16.2.1) and Chapter 13.
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18.17.16_5
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18.17.17
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18.17.37
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28: 30.6 Functions of Complex Argument
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►The solutions
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►of (30.2.1) with and are real when , and their principal values (§4.2(i)) are obtained by analytic continuation to .
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►with as in (30.11.4).
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