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11: 5.12 Beta Function
12: 20.2 Definitions and Periodic Properties
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§20.2(i) Fourier Series
… ►§20.2(ii) Periodicity and Quasi-Periodicity
… ►The theta functions are quasi-periodic on the lattice: … ►§20.2(iii) Translation of the Argument by Half-Periods
… ►§20.2(iv) -Zeros
…13: 14.20 Conical (or Mehler) Functions
§14.20 Conical (or Mehler) Functions
►§14.20(i) Definitions and Wronskians
… ► … ►§14.20(ii) Graphics
… ►§14.20(x) Zeros and Integrals
…14: 10.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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►The main functions treated in this chapter are the Bessel functions
, ; Hankel functions
, ; modified Bessel functions
, ; spherical Bessel functions
, , , ; modified spherical Bessel functions
, , ; Kelvin functions
, , , .
For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
…For the Kelvin functions the order is always assumed to be real.
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
15: 4.2 Definitions
16: 7.2 Definitions
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§7.2(i) Error Functions
… ► , , and are entire functions of , as is in the next subsection. … ►§7.2(ii) Dawson’s Integral
… ► , , and are entire functions of , as are and in the next subsection. … ►§7.2(iv) Auxiliary Functions
…17: 28.2 Definitions and Basic Properties
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28.2.1
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§28.2(ii) Basic Solutions ,
… ►§28.2(iv) Floquet Solutions
… ►§28.2(vi) Eigenfunctions
… ► …18: 28.20 Definitions and Basic Properties
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28.20.1
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►For other values of , , and the functions
, , are determined by analytic continuation.
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§28.20(iv) Radial Mathieu Functions ,
… ►§28.20(vi) Wronskians
… ►§28.20(vii) Shift of Variable
…19: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
►The function was introduced in Hurwitz (1882) and defined by the series expansion … ►As a function of , with () fixed, is analytic in the half-plane . The Riemann zeta function is a special case: …20: 25.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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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
.
nonnegative integers. | |
… | |
primes | on function symbols: derivatives with respect to argument. |