×

zbMATH — the first resource for mathematics

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

MSC:
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramowitz, A; Stegun, I.E, ()
[2] Ansel, P.R; Fisher, R.A, Note on the numerical evaluation of a Bessel function derivative, (), 54-56
[3] Apelblat, A, Some integrals of gamma, polygamma and Volterra functions, IMA J. appl. math., 34, 173-186, (1985) · Zbl 0583.33012
[4] Apelblat, A; Kravitsky, N, Integral representation of derivatives and integrals with respect to the order of the Bessel functions, J,(t), iv(t), the anger function jv(t) and the integral Bessel function jiv(t), IMA J. appl. math., 34, 187-210, (1985) · Zbl 0583.33006
[5] Erdélyi, A; Magnus, W; Oberhettinger, F; Tricomi, F.G, (), 217-227, Chap. 18.3
[6] Magnus, W; Oberhettinger, F; Soni, R.P, Formulas and theorems for the special functions of mathematical physics, (1966), Springer-Verlag Berlin · Zbl 0143.08502
[7] Oberhettinger, F, On the derivative of the Bessel functions with respect to the order, Stud. appl. math., 37, 75-78, (1958) · Zbl 0111.06607
[8] Oberhettinger, F; Badii, L, Tables of Laplace transforms, (1973), Springer-Verlag Berlin · Zbl 0285.65079
[9] Petiau, G, La théorie des fonctions de Bessel, (1955), Centre National de la Recherche Scientifique Paris · Zbl 0067.04704
[10] Watson, G.N, A treatise on the theory of Bessel functions, (1958), Cambridge Univ. Press Cambridge · Zbl 0174.36202
[11] Wienke, B.R, Order derivatives of Bessel functions, Bull. Calcutta math. soc., 69, 389-392, (1977) · Zbl 0412.33009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.