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11: 15.2 Definitions and Analytical Properties
§15.2(i) Gauss Series
The hypergeometric function F ( a , b ; c ; z ) is defined by the Gauss series … … On the circle of convergence, | z | = 1 , the Gauss series: …
§15.2(ii) Analytic Properties
12: 5.12 Beta Function
§5.12 Beta Function
Euler’s Beta Integral
See accompanying text
Figure 5.12.1: t -plane. Contour for first loop integral for the beta function. Magnify
See accompanying text
Figure 5.12.2: t -plane. Contour for second loop integral for the beta function. Magnify
Pochhammer’s Integral
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
(For other notation see Notation for the Special Functions.) … For the spherical Bessel functions and modified spherical Bessel functions the order n is a nonnegative integer. For the other functions when the order ν is replaced by n , it can be any integer. For the Kelvin functions the order ν is always assumed to be real. … 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
§4.2(iii) The Exponential Function
§4.2(iv) Powers
Powers with General Bases
16: 25.1 Special Notation
(For other notation see Notation for the Special Functions.)
k , m , n

nonnegative integers.

primes

on function symbols: derivatives with respect to argument.

The main function treated in this chapter is the Riemann zeta function ζ ( s ) . … The main related functions are the Hurwitz zeta function ζ ( s , a ) , the dilogarithm Li 2 ( z ) , the polylogarithm Li s ( z ) (also known as Jonquière’s function ϕ ( z , s ) ), Lerch’s transcendent Φ ( z , s , a ) , and the Dirichlet L -functions L ( s , χ ) .
17: 12.1 Special Notation
(For other notation see Notation for the Special Functions.) … Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values. The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: U ( a , z ) , V ( a , z ) , U ¯ ( a , z ) , and W ( a , z ) . …An older notation, due to Whittaker (1902), for U ( a , z ) is D ν ( z ) . …
18: 17.1 Special Notation
§17.1 Special Notation
(For other notation see Notation for the Special Functions.)
k , j , m , n , r , s

nonnegative integers.

Another function notation used is the ‘‘idem’’ function: …
19: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
§4.37(i) General Definitions
Each of the six functions is a multivalued function of z . …
Other Inverse Functions
§4.37(vi) Interrelations
20: 11.10 Anger–Weber Functions
§11.10 Anger–Weber Functions
§11.10(v) Interrelations
§11.10(vi) Relations to Other Functions
§11.10(viii) Expansions in Series of Products of Bessel Functions