Schläfli-type integrals

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1: 1.14 Integral Transforms
§1.14 Integral Transforms
where the last integral denotes the Cauchy principal value (1.4.25). … If $f(t)$ is absolutely integrable on $[0,R]$ for every finite $R$, and the integral (1.14.47) converges, then …
§1.14(viii) Compendia
For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).
3: 10.64 Integral Representations
Schläfli-TypeIntegrals
10.64.1 $\operatorname{ber}_{n}\left(x\sqrt{2}\right)=\frac{(-1)^{n}}{\pi}\int_{0}^{\pi% }\cos\left(x\sin t-nt\right)\cosh\left(x\sin t\right)\,\mathrm{d}t,$
10.64.2 $\operatorname{bei}_{n}\left(x\sqrt{2}\right)=\frac{(-1)^{n}}{\pi}\int_{0}^{\pi% }\sin\left(x\sin t-nt\right)\sinh\left(x\sin t\right)\,\mathrm{d}t.$
4: 6.2 Definitions and Interrelations
§6.2(i) Exponential and Logarithmic Integrals
The logarithmic integral is defined by …
8: 19.16 Definitions
§19.16(i) Symmetric Integrals
All other elliptic cases are integrals of the second kind. …(Note that $R_{C}\left(x,y\right)$ is not an elliptic integral.) … Each of the four complete integrals (19.16.20)–(19.16.23) can be integrated to recover the incomplete integral: …
10: 19.2 Definitions
§19.2(i) General Elliptic Integrals
is called an elliptic integral. …