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标题：Some Properties of Multiple Generalized <i>q</i>-Genocchi Polynomials with Weight <svg style="vertical-align:-0.216pt;width:15.2375px;" id="M1" height="11.85" version="1.1" viewBox="0 0 15.2375 11.85" width="15.2375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.022,-0,0,-.022,.625,10.963)"> <path id="x1D736" d="M505 450h125l-163 -259q-1 -4 -1 -12q0 -19 1 -23q9 -98 41 -98q36 0 58 76l24 -7q-34 -139 -121 -139q-32 0 -57.5 24t-31.5 55q-72 -77 -181 -77q-73 0 -114 44t-41 124q0 118 79 210q79 93 197 93q51 0 86 -27t50 -71zM369 281q0 141 -62 141q-43 0 -95 -84
q-52 -82 -52 -195q0 -50 15 -83t42 -33q35 0 79 57q43 58 67 121q6 35 6 76z"/> </g> </svg> and Weak Weight <svg style="vertical-align:-3.69pt;width:13.6875px;" id="M2" height="21.200001" version="1.1" viewBox="0 0 13.6875 21.200001" width="13.6875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.022,-0,0,-.022,.625,15.975)"> <path id="x1D737" d="M54 -114l114 487q24 102 62.5 165t102.5 109q53 38 129 38q51 0 86 -33.5t35 -84.5q0 -57 -31.5 -105t-81.5 -68v-2q88 -14 88 -126q0 -64 -29 -127q-29 -62 -90 -107q-62 -44 -143 -44q-67 0 -97 18l-28 -124q-11 -51 -26 -87h-117q9 19 26 91zM304 480l-87 -393
q0 -29 19 -44t48 -15q63 0 110 74q46 74 46 153q0 117 -52 117q-6 0 -23.5 -3t-21.5 -3q-33 0 -33 25q0 15 15 25.5t41 10.5q8 0 30 -6q27 -5 28 -5q26 0 41 43t15 89q0 39 -17.5 62t-44.5 23q-46 0 -71 -35.5t-43 -117.5z"/> </g> </svg>
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作者：J. Y. Kang
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/179385
出版社：Hindawi Publishing Corporation
摘要：The present paper deals with the various q-Genocchi numbers and polynomials. We define a new type of multiple generalized q-Genocchi numbers and polynomials with weight α and weak weight β by applying the method of p-adic q-integral. We will find a link between their numbers and polynomials with weight α and weak weight β. Also we will obtain the interesting properties of their numbers and polynomials with weight α and weak weight β. Moreover, we construct a Hurwitz-type zeta function which interpolates multiple generalized q-Genocchi polynomials with weight α and weak weight β and find some combinatorial relations.