integrals of vector-valued functions

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21: 19.2 Definitions

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§19.2(i) General Elliptic Integrals

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§19.2(ii) Legendre’s Integrals

… ►The principal values of $K\left(k\right)$ and $E\left(k\right)$ are even functions. … ►

§19.2(iii) Bulirsch’s Integrals

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§19.2(iv) A Related Function: $R_C(x,y)$

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22: 1.6 Vectors and Vector-Valued Functions

§1.6 Vectors and Vector-Valued Functions

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§1.6(iii) Vector-Valued Functions

… ►The path integral of a continuous function $f(x,y,z)$ is … ►

Stokes’s Theorem

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23: 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 $\nu$ is replaced by $n$, it can be any integer. For the Kelvin functions the order $\nu$ 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).

24: 4.2 Definitions

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§4.2(iii) The Exponential Function

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§4.2(iv) Powers

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Powers with General Bases

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25: 25.11 Hurwitz Zeta Function

§25.11 Hurwitz Zeta Function

… ►The Riemann zeta function is a special case: … ►

§25.11(vii) Integral Representations

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§25.11(viii) Further Integral Representations

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§25.11(ix) Integrals

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26: 11.10 Anger–Weber Functions

§11.10 Anger–Weber Functions

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§11.10(i) Definitions

… ►For the Fresnel integrals $C$ and $S$ see §7.2(iii). … ►

§11.10(x) Integrals and Sums

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27: 8.17 Incomplete Beta Functions

§8.17 Incomplete Beta Functions

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§8.17(ii) Hypergeometric Representations

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§8.17(iii) Integral Representation

… ►Further integral representations can be obtained by combining the results given in §8.17(ii) with §15.6. … ►

§8.17(vi) Sums

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28: 1.10 Functions of a Complex Variable

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§1.10(viii) Functions Defined by Contour Integrals

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§1.10(xi) Generating Functions

… ►Then $F(x;z)$ is the generating function for the functions $p_n(x)$, which will automatically have an integral representation …

29: 4.37 Inverse Hyperbolic Functions

§4.37 Inverse Hyperbolic Functions

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§4.37(i) General Definitions

… ►Each of the six functions is a multivalued function of $z$. … ►

Other Inverse Functions

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§4.37(vi) Interrelations

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30: 4.23 Inverse Trigonometric Functions

§4.23 Inverse Trigonometric Functions

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§4.23(i) General Definitions

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Other Inverse Functions

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§4.23(viii) Gudermannian Function

… ►The inverse Gudermannian function is given by …