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Green theorem for vector-valued functions

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1: 1.6 Vectors and Vector-Valued Functions
Green’s Theorem
Stokes’s Theorem
Gauss’s (or Divergence) Theorem
Green’s Theorem (for Volume)
2: 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
3: 9.1 Special Notation
(For other notation see Notation for the Special Functions.)
k nonnegative integer, except in §9.9(iii).
The main functions treated in this chapter are the Airy functions Ai ( z ) and Bi ( z ) , and the Scorer functions Gi ( z ) and Hi ( z ) (also known as inhomogeneous Airy functions). Other notations that have been used are as follows: Ai ( x ) and Bi ( x ) for Ai ( x ) and Bi ( x ) (Jeffreys (1928), later changed to Ai ( x ) and Bi ( x ) ); U ( x ) = π Bi ( x ) , V ( x ) = π Ai ( x ) (Fock (1945)); A ( x ) = 3 1 / 3 π Ai ( 3 1 / 3 x ) (Szegő (1967, §1.81)); e 0 ( x ) = π Hi ( x ) , e ~ 0 ( x ) = π Gi ( x ) (Tumarkin (1959)).
4: 31.1 Special Notation
(For other notation see Notation for the Special Functions.)
x , y real variables.
The main functions treated in this chapter are H ( a , q ; α , β , γ , δ ; z ) , ( s 1 , s 2 ) 𝐻𝑓 m ( a , q m ; α , β , γ , δ ; z ) , ( s 1 , s 2 ) 𝐻𝑓 m ν ( a , q m ; α , β , γ , δ ; z ) , and the polynomial 𝐻𝑝 n , m ( a , q n , m ; n , β , γ , δ ; z ) . …Sometimes the parameters are suppressed.
5: 23.15 Definitions
§23.15 Definitions
§23.15(i) General Modular Functions
Elliptic Modular Function
Dedekind’s Eta Function (or Dedekind Modular Function)
6: 5.15 Polygamma Functions
§5.15 Polygamma Functions
The functions ψ ( n ) ( z ) , n = 1 , 2 , , are called the polygamma functions. In particular, ψ ( z ) is the trigamma function; ψ ′′ , ψ ( 3 ) , ψ ( 4 ) are the tetra-, penta-, and hexagamma functions respectively. Most properties of these functions follow straightforwardly by differentiation of properties of the psi function. … For B 2 k see §24.2(i). …
7: 5.2 Definitions
§5.2(i) Gamma and Psi Functions
Euler’s Integral
5.2.1 Γ ( z ) = 0 e t t z 1 d t , z > 0 .
It is a meromorphic function with no zeros, and with simple poles of residue ( 1 ) n / n ! at z = n . …
5.2.2 ψ ( z ) = Γ ( z ) / Γ ( z ) , z 0 , 1 , 2 , .
8: 9.12 Scorer Functions
§9.12 Scorer Functions
where …
§9.12(ii) Graphs
Functions and Derivatives
9: 14.19 Toroidal (or Ring) Functions
§14.19 Toroidal (or Ring) Functions
§14.19(i) Introduction
§14.19(ii) Hypergeometric Representations
§14.19(iv) Sums
§14.19(v) Whipple’s Formula for Toroidal Functions
10: 11.9 Lommel Functions
§11.9 Lommel Functions
Reflection Formulas
§11.9(ii) Expansions in Series of Bessel Functions