Identities for the exponential integral and the complementary error transforms

Brown, D. J. A.; Dernek, Neşe; Yürekli, Osman

doi:10.1016/j.amc.2006.05.024

Cited by 8 publications

(4 citation statements)

References 2 publications

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“…introduced in Brown et al (2007a, p. 1377 (1.1)), E 2,1 -transform defined by (2.51) introduced in Brown et al (2007b, p. 1557 (1.1)) and the Widder transform defined by…”

Section: Corollarymentioning

confidence: 99%

“…Subsequently, various Parseval-Goldstein type identities were given in (for example) Brown et al (2007a), Brown et al (2007b), Dernek et al (2007), Glasser (1973), , and for the L 2 -transform. New solutions techniques were obtained for the Bessel differential equation in Yürekli & Wilson (2002) and the Hermite differential equation in Yürekli & Wilson (2003) using this integral transform.…”

Section: Introductionmentioning

confidence: 99%

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Identities for the Glasser transform and their applications

Dernek¹,

Dernek²,

Yürekli³

2012

Contemporary Analysis and Applied Mathematics

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In the present paper the authors show that an iteration of the L 2 -transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for L 2 -transform and the Glasser transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

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“…introduced in Brown et al (2007a, p. 1377 (1.1)), E 2,1 -transform defined by (2.51) introduced in Brown et al (2007b, p. 1557 (1.1)) and the Widder transform defined by…”

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Identities for the Glasser transform and their applications

Dernek¹,

Dernek²,

Yürekli³

2012

Contemporary Analysis and Applied Mathematics

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“…The exponential integral transform (third iterate of the Laplace transform) [6] (1.11) where E 1 (x) is the exponential integral function 12) and f ∈ L loc …”

Section: Introductionmentioning

confidence: 99%

Some results involving integral transforms of Airy functions

Ansari

Masomi

2015

Integral Transforms and Special Functions

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“…2p) ,(3,2) ,(1,1) (1 + υ + µ, 2µ) , Γ (1 − β) Γ (1 + β) Γ (γ − p (1 + β)) Γ (1 + ν − µ (1 + β)) (γ, 2p) , (1 + α, 2) , (1, 1) (1 + v, 2µ) , (γ + p, 2p) , (2 + α, 2) , (1, 1) (1 + v + µ, 2µ) , (2, 2) Γ (1 − β) Γ (α + β) Γ (γ − p (α + β)) Γ (1 + ν − µ (α + β)) y α+β+1 . (3.9)If we set f (t) = t β−1 , (0 < Reβ < 1) in (2.25) of Corollary 2.13 and use formulas (2.9) and [5, p.68, Eq(1)], then we obtain (3.9).…”

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confidence: 99%