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Apelblat, Alexander

Derivatives and integrals with respect to the order of the Struve functions \(H_{\nu}(x)\) and \(L_{\nu}(x)\). (English) Zbl 0669.33009

J. Math. Anal. Appl. 137, No. 1, 17-36 (1989).
In continuation of similar work for \(J_{\nu}\), the author obtains these derivatives and integrals (from 0 to \(\infty)\) in the form of integrals by differentiating or integrating, respectively, an integral representation of the given functions, or by the Laplace transform method. Results for \(L_{\nu}\) are obtained from those for \(H_{\nu}\) by the familiar relation between these two functions. 5S-tables of the associated Volterra function and of some auxiliary integrals are included.
Reviewer: E.Kreyszig

Cited in 1 Document

MSC:

33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

cylinder functions; Bessel functions; Struve functions
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\textit{A. Apelblat}, J. Math. Anal. Appl. 137, No. 1, 17--36 (1989; Zbl 0669.33009)
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Digital Library of Mathematical Functions:

§11.4(vi) Derivatives with Respect to Order ‣ §11.4 Basic Properties ‣ Struve and Modified Struve Functions ‣ Chapter 11 Struve and Related Functions
§11.7(iv) Integrals with Respect to Order ‣ §11.7 Integrals and Sums ‣ Struve and Modified Struve Functions ‣ Chapter 11 Struve and Related Functions

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