Intriguing integrals: an Euler-inspired odyssey

Lord, Nick

doi:10.1017/s0025557200182063

Cited by 11 publications

(13 citation statements)

References 12 publications

(9 reference statements)

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“…Furthermore, since and as , the right-hand side of (2) takes the form of a Riemann sum of terms with element , which tends to the definite integral as (see [2]). …”

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confidence: 99%

99.33 An integral inequality with applications to probability theory

Krasopoulos¹

2015

Math. Gaz.

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“…Furthermore, since and as , the right-hand side of (2) takes the form of a Riemann sum of terms with element , which tends to the definite integral as (see [2]). …”

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confidence: 99%

99.33 An integral inequality with applications to probability theory

Krasopoulos¹

2015

Math. Gaz.

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“…The following identities are unashamedly repeated from [3, p. 421]. However, we are approaching them from the opposite direction: the emphasis in [3] was on finding interesting formulae for γ, while ours is on evaluation of series involving ζ(n).…”

Section: Application 3: We Havementioning

confidence: 99%

Series involving ζ(n)

Jameson¹

2014

Math Gaz

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“…It must be admitted that we have lost the beautiful simplicity of the original non-proof, but even as amended the method still stands comparison with other methods for the sine integral (e.g. [2,3,6,7]). It has done more than just evaluate the integral: it has also established the inequality , where , which is of some interest in its own right.…”

Section: Wherementioning

confidence: 99%

Using double integrals to solve single integrals

Jameson¹

2016

Math. Gaz.

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Consider the integralwhere b > a > 0. First, let us clarify why it even exists. Of course, convergence at infinity is ensured by the exponential terms, but the integrals of and e–ax/x and e–bx/x, taken separately, are divergent at 0, since these integrands equate asymptotically to 1/x as x → 0. However,so (e–ax – e–bx)/x tends to the finite limit b – a as x → 0 and there is no problem integrating it on intervals of the form [0, r].A neat way to evaluate I1 starts by expressing the integrand itself as an integral:(1)Inserting this into I1 converts it into a double integral.

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Intriguing integrals: an Euler-inspired odyssey

Cited by 11 publications

References 12 publications

99.33 An integral inequality with applications to probability theory

99.33 An integral inequality with applications to probability theory

Series involving ζ(n)

Using double integrals to solve single integrals

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