Struve functions

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21: 10.43 Integrals

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10.43.2 $$\int z^{\nu }{𝒵}_{\nu }\left(z\right)dz={\pi }^{\frac{1}{2}}{2}^{\nu -1}\mathrm{\Gamma }\left(\nu +\frac{1}{2}\right)z\left({𝒵}_{\nu }\left(z\right){𝐋}_{\nu -1}\left(z\right)-{𝒵}_{\nu -1}\left(z\right){𝐋}_{\nu }\left(z\right)\right),$$ $\nu \ne -\frac{1}{2}$.

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\int$: integral, ${𝐋}_{\nu }\left(z\right)$: modified Struve function, ${𝒵}_{\nu }\left(z\right)$: modified cylinder function, $z$: complex variable and $\nu$: complex parameter

A&S Ref:

11.1.8 (Case $\nu =0$ only)

Referenced by:

§10.43(i)

Permalink:

http://dlmf.nist.gov/10.43.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §10.43(i), §10.43 and Ch.10

►For the modified Struve function ${𝐋}_{\nu }\left(z\right)$ see §11.2(i). …

22: 10.22 Integrals

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10.22.2 $$\int z^{\nu }{𝒞}_{\nu }\left(z\right)dz={\pi }^{\frac{1}{2}}{2}^{\nu -1}\mathrm{\Gamma }\left(\nu +\frac{1}{2}\right)z\left({𝒞}_{\nu }\left(z\right){𝐇}_{\nu -1}\left(z\right)-{𝒞}_{\nu -1}\left(z\right){𝐇}_{\nu }\left(z\right)\right),$$ $\nu \ne -\frac{1}{2}$.

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, ${𝐇}_{\nu }\left(z\right)$: Struve function, $\pi$: the ratio of the circumference of a circle to its diameter, ${𝒞}_{\nu }\left(z\right)$: cylinder function, $dx$: differential of $x$ , $\int$: integral, $z$: complex variable and $\nu$: complex parameter

A&S Ref:

11.17 (Case $\nu =0$ only)

Permalink:

http://dlmf.nist.gov/10.22.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §10.22(i), §10.22 and Ch.10

►For the Struve function ${𝐇}_{\nu }\left(z\right)$ see §11.2(i). …

23: Software Index

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	Open Source													With Book						Commercial
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11 Struve and Related Functions
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24: Bibliography S

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The real zeros of Struve’s function. SIAM J. Math. Anal. 1 (3), pp. 365–375.

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External Links:

Document, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§11.4(vii).

Encodings:

BibTeX

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25: Bibliography M

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Chebyshev expansions for modified Struve and related functions. Math. Comp. 60 (202), pp. 735–747.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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