\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{Graham}
\citation{T}
\citation{B}
\citation{Diletal}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{2}{{1}{1}{Introduction}{equation.1.1}{}}
\newlabel{10}{{2}{1}{Introduction}{equation.1.2}{}}
\citation{Da}
\citation{Gr}
\citation{T}
\citation{B}
\citation{B2}
\citation{B3}
\citation{B4}
\citation{Dil1}
\citation{MEZO}
\citation{B}
\citation{Dil2}
\citation{Kargin}
\citation{Mezo2}
\citation{Agoh}
\citation{Chu}
\citation{Kamano}
\citation{Komatsu}
\citation{Komatsu2}
\citation{Singh}
\citation{Zhao}
\citation{Hansel}
\citation{Agoh2}
\citation{B2}
\citation{Dagli1}
\citation{Kim}
\citation{Liu}
\citation{Norlund}
\citation{Diletal}
\newlabel{11}{{3}{2}{Introduction}{equation.1.3}{}}
\newlabel{14}{{4}{2}{Introduction}{equation.1.4}{}}
\newlabel{1}{{5}{2}{Introduction}{equation.1.5}{}}
\newlabel{b1}{{6}{2}{Introduction}{equation.1.6}{}}
\newlabel{b2}{{7}{2}{Introduction}{equation.1.7}{}}
\citation{KELLER}
\newlabel{5}{{8}{3}{Introduction}{equation.1.8}{}}
\newlabel{6}{{9}{3}{Introduction}{equation.1.9}{}}
\newlabel{26}{{10}{3}{Introduction}{equation.1.10}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Sums of products of geometric polynomials}{3}{section.2}}
\newlabel{sec2}{{2}{3}{Sums of products of geometric polynomials}{section.2}{}}
\newlabel{8}{{11}{3}{Sums of products of geometric polynomials}{equation.2.11}{}}
\newlabel{29}{{12}{3}{Sums of products of geometric polynomials}{equation.2.12}{}}
\citation{Diletal}
\newlabel{3}{{13}{4}{Sums of products of geometric polynomials}{equation.2.13}{}}
\newlabel{4}{{14}{4}{Sums of products of geometric polynomials}{equation.2.14}{}}
\newlabel{7}{{15}{4}{Sums of products of geometric polynomials}{equation.2.15}{}}
\newlabel{9}{{16}{4}{Sums of products of geometric polynomials}{equation.2.16}{}}
\citation{BoyadzhievandDil}
\newlabel{teo1}{{1}{5}{}{theorem.1}{}}
\newlabel{13}{{17}{5}{}{equation.2.17}{}}
\newlabel{12}{{18}{5}{}{equation.2.18}{}}
\newlabel{23}{{19}{5}{}{equation.2.19}{}}
\newlabel{69}{{20}{5}{Sums of products of geometric polynomials}{equation.2.20}{}}
\citation{GuoandQi}
\citation{BoyadzhievandDil}
\newlabel{18}{{21}{6}{Sums of products of geometric polynomials}{equation.2.21}{}}
\newlabel{19}{{22}{6}{Sums of products of geometric polynomials}{equation.2.22}{}}
\newlabel{teo4}{{3}{6}{}{theorem.3}{}}
\newlabel{21}{{23}{6}{}{equation.2.23}{}}
\newlabel{15}{{24}{6}{Sums of products of geometric polynomials}{equation.2.24}{}}
\newlabel{17}{{4}{6}{}{theorem.4}{}}
\newlabel{teo5}{{5}{6}{}{theorem.5}{}}
\newlabel{84}{{25}{6}{}{equation.2.25}{}}
\newlabel{85}{{26}{6}{}{equation.2.26}{}}
\newlabel{86}{{27}{6}{}{equation.2.27}{}}
\citation{Graham}
\newlabel{79}{{28}{7}{Sums of products of geometric polynomials}{equation.2.28}{}}
\newlabel{80}{{29}{7}{Sums of products of geometric polynomials}{equation.2.29}{}}
\newlabel{81}{{30}{7}{Sums of products of geometric polynomials}{equation.2.30}{}}
\newlabel{82}{{31}{7}{Sums of products of geometric polynomials}{equation.2.31}{}}
\newlabel{24}{{32}{7}{Sums of products of geometric polynomials}{equation.2.32}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Integrals of products of geometric polynomials}{7}{section.3}}
\newlabel{sec3}{{3}{7}{Integrals of products of geometric polynomials}{section.3}{}}
\newlabel{lem1}{{6}{7}{}{theorem.6}{}}
\newlabel{25}{{33}{7}{}{equation.3.33}{}}
\newlabel{lem2}{{7}{8}{}{theorem.7}{}}
\newlabel{33}{{34}{8}{}{equation.3.34}{}}
\citation{Graham}
\citation{Graham}
\citation{Rahmani}
\citation{Andrews}
\newlabel{teo2}{{8}{10}{}{theorem.8}{}}
\newlabel{30}{{35}{10}{}{equation.3.35}{}}
\newlabel{27}{{36}{10}{Integrals of products of geometric polynomials}{equation.3.36}{}}
\citation{APOSTOL}
\citation{B3}
\citation{GuoandQi}
\citation{KimandHu}
\newlabel{28}{{3}{11}{Integrals of products of geometric polynomials}{equation.3.36}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Applications}{11}{section.4}}
\newlabel{sec4}{{4}{11}{Applications}{section.4}{}}
\newlabel{53}{{37}{11}{Applications}{equation.4.37}{}}
\newlabel{22}{{38}{11}{Applications}{equation.4.38}{}}
\bibcite{Andrews}{1}
\bibcite{Agoh}{2}
\bibcite{Agoh2}{3}
\bibcite{APOSTOL}{4}
\bibcite{B}{5}
\bibcite{B2}{6}
\bibcite{B3}{7}
\@writefile{toc}{\contentsline {section}{\numberline {5}Acknowledgments}{12}{section.5}}
\bibcite{B4}{8}
\bibcite{BoyadzhievandDil}{9}
\bibcite{Chu}{10}
\bibcite{Dagli1}{11}
\bibcite{Da}{12}
\bibcite{Diletal}{13}
\bibcite{Dil1}{14}
\bibcite{Dil2}{15}
\bibcite{Graham}{16}
\bibcite{Gr}{17}
\bibcite{GuoandQi}{18}
\bibcite{Hansel}{19}
\bibcite{Kargin}{20}
\bibcite{Kamano}{21}
\bibcite{KELLER}{22}
\bibcite{KimandHu}{23}
\bibcite{Kim}{24}
\bibcite{Komatsu}{25}
\bibcite{Komatsu2}{26}
\bibcite{Liu}{27}
\bibcite{MEZO}{28}
\bibcite{Mezo2}{29}
\bibcite{Norlund}{30}
\bibcite{Rahmani}{31}
\bibcite{Singh}{32}
\bibcite{T}{33}
\bibcite{Zhao}{34}
