Euler%20totient
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31—40 of 452 matching pages
31: Software Index
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5.24(ii) , | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | FDLIBM |
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5.24(vi) , | ✓ | ✓ | ✓ | ✓ | a | ✓ | ✓ | ✓ | ✓ | a | |||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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24 Bernoulli and Euler Polynomials | |||||||||||||||||||||||||
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32: 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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(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 .
33: 16.15 Integral Representations and Integrals
34: 30.1 Special Notation
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►The main functions treated in this chapter are the eigenvalues and the spheroidal wave functions , , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
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►Flammer (1957) and Abramowitz and Stegun (1964) use for , for , and
…where is a normalization constant determined by
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real variable. Except in §§30.7(iv), 30.11(ii), 30.13, and 30.14, . | |
real parameter (positive, zero, or negative). | |
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35: 20.10 Integrals
36: 8 Incomplete Gamma and Related
Functions
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37: 28 Mathieu Functions and Hill’s Equation
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38: 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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39: 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, …40: 7.23 Tables
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Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.