English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In a previous paper (see [5]), we applied a fixed δ-sequence and neutrix limit due to Vander Corput to give meaning to distributions δk and (δ′)k for k∈(0,1) and k=2,3,…. In this paper,we choose a fixed analytic branch such that zα(−π<argz≤π) is an analytic single-valued function anddefine δα(z) on a suitable function space Ia. We show that δα(z)∈I′a. Similar results on (δ(m)(z))α areobtained. Finally, we use the Hilbert integral φ(z)=1πi∫−∞+∞φ(t)t−zdt where φ(t)∈D(R), to redefine δn(x)as a boundary value of δn(z−i ϵ ). The definition of δn(x) is independent of the choice of δ-sequence

international journal of mathematics and mathematical sciences

On defining the generalized functions<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta ^\alpha \left( z \right)$"><mml:msup><mml:mi>δ</mml:mi><mml:mi>α</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\delta ^n \left( x \right)$"><mml:msup><mml:mi>δ</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:…

On defining the generalized functionsδα(z)andδn(x)