Calculating Zeros of the <svg style="vertical-align:-4.626pt;width:11.125px;" id="M1" height="15.925" version="1.1" viewBox="0 0 11.125 15.925" width="11.125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,10.1)"><path id="x1D45E" d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387
q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z"/></g>

		
	
</svg>-Genocchi Polynomials Associated with <svg style="vertical-align:-4.626pt;width:13.4125px;" id="M2" height="17.5" version="1.1" viewBox="0 0 13.4125 17.5" width="13.4125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,11.675)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z"/></g>

		
	
</svg>-Adic
<svg style="vertical-align:-4.626pt;width:11.125px;" id="M3" height="15.925" version="1.1" viewBox="0 0 11.125 15.925" width="11.125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,10.1)"><use xlink:href="#x1D45E"/></g>

		
	
</svg>-Integral on
<svg style="vertical-align:-7.55826pt;width:26.799999px;" id="M4" height="24.6625" version="1.1" viewBox="0 0 26.799999 24.6625" width="26.799999"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,15.188)"><path id="x2124" d="M734 170q-25 -130 -36 -170h-661l-8 15l420 599h-173q-77 0 -102 -7t-39 -29q-19 -29 -35 -87l-29 1l12 183h24q9 -16 19 -20.5t34 -4.5h543l7 -14l-416 -598l166 -2q94 0 131.5 7.5t58.5 29.5q28 29 55 103zM639 614h-89l-397 -567l88 -7z"/></g>

			<g transform="matrix(.016,0,0,-.016,16.813,20.575)"><use xlink:href="#x1D45D"/></g>

		
	
</svg>

<table>Stacks of zeros <svg height="18.25" id="M222" style="vertical-align:-4.8335pt" version="1.1" viewbox="0 0 162.175 18.25" width="162.175" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,12.163)"><path d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" id="x1D43A"></path></g>
<g transform="matrix(.012,0,0,-.012,12.375,16.25)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.012,0,0,-.012,18.348,16.25)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.012,0,0,-.012,21.061,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.012,0,0,-.012,26.772,16.25)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.012,0,0,-.012,31.675,16.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
<g transform="matrix(.017,0,0,-.017,38,12.163)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,0,0,-.017,43.882,12.163)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g><g transform="matrix(.017,0,0,-.017,53.384,12.163)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
<g transform="matrix(.017,0,0,-.017,64.938,12.163)"><path d="M54 437h47v21q0 48 11 83q23 72 77 118q55 46 110 53q53 -3 79 -34q13 -16 5 -35q-5 -13 -19 -24t-27 3q-37 37 -81 37q-34 0 -53 -29q-24 -37 -23 -153v-40h118q5 -7 1.5 -21t-11.5 -19h-108v-287q0 -55 13 -67t73 -18v-25h-236v26q49 5 60 16.5t11 60.5v294h-70l-4 11z
" id="x66"></path></g><g transform="matrix(.017,0,0,-.017,69.816,12.163)"><path d="M257 449q92 0 154 -65t62 -158q0 -112 -67 -175t-150 -63q-98 0 -158.5 66.5t-60.5 154.5q0 59 21 106.5t54.5 75.5t71 43t73.5 15zM244 416q-48 0 -81 -47t-33 -128q0 -96 38 -158t99 -62q51 0 82 43.5t31 139.5q0 91 -36 151.5t-100 60.5z" id="x6F"></path></g><g transform="matrix(.017,0,0,-.017,78.282,12.163)"><path d="M181 342h2q63 107 121 107q24 0 41 -16t17 -34q0 -34 -32 -49q-17 -7 -26 2q-21 20 -43 20q-20 0 -42 -22t-38 -63v-183q0 -50 12.5 -62t69.5 -16v-26h-230v26q47 5 58 17t11 61v207q0 49 -9 60.5t-53 16.5v23q74 12 141 40v-109z" id="x72"></path></g>
<g transform="matrix(.017,0,0,-.017,90.25,12.163)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,0,0,-.017,103.118,12.163)"><path d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" id="x2264"></path></g><g transform="matrix(.017,0,0,-.017,117.822,12.163)"><path d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g><g transform="matrix(.017,0,0,-.017,131.081,12.163)"><path d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" id="x2264"></path></g><g transform="matrix(.017,0,0,-.017,145.785,12.163)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g><g transform="matrix(.017,0,0,-.017,153.944,12.163)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg>.</table>

International Journal of Mathematics and Mathematical Sciences

fig14

Figure 14

Figure 14: Calculating Zeros of the <svg style="vertical-align:-4.626pt;width:11.125px;" id="M1" height="15.925" version="1.1" viewBox="0 0 11.125 15.925" width="11.125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,10.1)"><path id="x1D45E" d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387
q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z"/></g>

		
	
</svg>-Genocchi Polynomials Associated with <svg style="vertical-align:-4.626pt;width:13.4125px;" id="M2" height="17.5" version="1.1" viewBox="0 0 13.4125 17.5" width="13.4125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,11.675)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z"/></g>

		
	
</svg>-Adic
<svg style="vertical-align:-4.626pt;width:11.125px;" id="M3" height="15.925" version="1.1" viewBox="0 0 11.125 15.925" width="11.125"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,10.1)"><use xlink:href="#x1D45E"/></g>

		
	
</svg>-Integral on
<svg style="vertical-align:-7.55826pt;width:26.799999px;" id="M4" height="24.6625" version="1.1" viewBox="0 0 26.799999 24.6625" width="26.799999"      xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,0,0,-.022,.062,15.188)"><path id="x2124" d="M734 170q-25 -130 -36 -170h-661l-8 15l420 599h-173q-77 0 -102 -7t-39 -29q-19 -29 -35 -87l-29 1l12 183h24q9 -16 19 -20.5t34 -4.5h543l7 -14l-416 -598l166 -2q94 0 131.5 7.5t58.5 29.5q28 29 55 103zM639 614h-89l-397 -567l88 -7z"/></g>

			<g transform="matrix(.016,0,0,-.016,16.813,20.575)"><use xlink:href="#x1D45D"/></g>

		
	
</svg> 

Figure 14 | Calculating Zeros of the 
	
		
			

		
	
-Genocchi Polynomials Associated with 
	
		
			

		
	
-Adic

	
		
			

		
	
-Integral on

	
		
			

			

		
	
 

International Journal of Mathematics and Mathematical Sciences

Calculating Zeros of the -Genocchi Polynomials Associated with -Adic -Integral on

Figure 14