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representations. 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PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/67424232/A_new_class_of_generalized_Bernoulli_polynomials_and_Euler_polynomials"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="104356855" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/104356855/Multiple_Poly_Bernoulli_Polynomials_of_the_Second_Kind_Associated_with_Hermite_Polynomials">Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="107434744" href="https://independent.academia.edu/mohdghayasuddin">mohd ghayasuddin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fasciculi Mathematici, 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multiple-Poly-Bernoulli Polynomials of the Second Kind Associated with Hermite Polynomials","attachmentId":104109549,"attachmentType":"pdf","work_url":"https://www.academia.edu/104356855/Multiple_Poly_Bernoulli_Polynomials_of_the_Second_Kind_Associated_with_Hermite_Polynomials","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/104356855/Multiple_Poly_Bernoulli_Polynomials_of_the_Second_Kind_Associated_with_Hermite_Polynomials"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="50434314" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50434314/Certain_Identities_Associated_with_p_q_Binomial_Coefficients_and_p_q_Stirling_Polynomials_of_the_Second_Kind">Certain Identities Associated with (p,q)-Binomial Coefficients and (p,q)-Stirling Polynomials of the Second Kind</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="71989141" href="https://independent.academia.edu/TalhaUsman5">Talha Usman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Symmetry</p><p class="ds-related-work--abstract ds2-5-body-sm">The q-Stirling numbers (polynomials) of the second kind have been investigated and applied in a variety of research subjects including, even, the q-analogue of Bernstein polynomials. The (p,q)-Stirling numbers (polynomials) of the second kind have been studied, particularly, in relation to combinatorics. In this paper, we aim to introduce new (p,q)-Stirling polynomials of the second kind which are shown to be fit for the (p,q)-analogue of Bernstein polynomials. We also present some interesting identities involving the (p,q)-binomial coefficients. We further discuss certain vanishing identities associated with the q-and (p,q)-Stirling polynomials of the second kind.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Certain Identities Associated with (p,q)-Binomial Coefficients and (p,q)-Stirling Polynomials of the Second Kind","attachmentId":68424478,"attachmentType":"pdf","work_url":"https://www.academia.edu/50434314/Certain_Identities_Associated_with_p_q_Binomial_Coefficients_and_p_q_Stirling_Polynomials_of_the_Second_Kind","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50434314/Certain_Identities_Associated_with_p_q_Binomial_Coefficients_and_p_q_Stirling_Polynomials_of_the_Second_Kind"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":75501373,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":75501373,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_75501373" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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