functions s(ϵ,ℓ;r),c(ϵ,ℓ;r)
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1: 7.2 Definitions
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7.2.8
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, , and are entire functions of , as are and in the next subsection.
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7.2.10
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7.2.11
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2: 22.16 Related Functions
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§22.16(ii) Jacobi’s Epsilon Function
►Integral Representations
… ►Relation to Theta Functions
… ►§22.16(iii) Jacobi’s Zeta Function
►Definition
…3: 28.2 Definitions and Basic Properties
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§28.2(ii) Basic Solutions ,
… ►§28.2(iv) Floquet Solutions
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28.2.18
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§28.2(vi) Eigenfunctions
…4: 28.20 Definitions and Basic Properties
5: 19.2 Definitions
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►Let be a cubic or quartic polynomial in with simple zeros, and let be a rational function of and containing at least one odd power of .
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19.2.1
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19.2.2
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19.2.17
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19.2.21
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6: 25.1 Special Notation
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►The main function treated in this chapter is the Riemann zeta function
.
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►The main related functions are the Hurwitz zeta function
, the dilogarithm , the polylogarithm (also known as Jonquière’s function
), Lerch’s transcendent , and the Dirichlet -functions
.
7: 31.6 Path-Multiplicative Solutions
8: 4.44 Other Applications
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►The Einstein functions and Planck’s radiation function are elementary combinations of exponentials, or exponentials and logarithms.
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9: 31.4 Solutions Analytic at Two Singularities: Heun Functions
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►To emphasize this property this set of functions is denoted by
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31.4.1
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31.4.3
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►The set depends on the choice of and .
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10: 31.1 Special Notation
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►The main functions treated in this chapter are , , , and the polynomial .
…Sometimes the parameters are suppressed.