右辺＝(π/(8a^3)){tanh(aπ/2)-aπ/2・sech^2(aπ/2)}

　ｓｉｎｈ（ｉｘ）＝ｉｓｉｎｘ

　ｃｏｓｈ（ｉｘ）＝ｃｏｓｘ

　ｔａｎｈ（ｉｘ）＝ｉｔａｎｘ

より，ａ→ａｉとおくと

＝(-iπ/(8a^3)){itan(aπ/2)-aiπ/2・sec^2(aπ/2)}

＝(π/(8a^3)){tan(aπ/2)-aπ/2・sec^2(aπ/2)}

　ａ＝１／２とおくと，＝π{π/2-1}

左辺＝（ｐ^2／２ｑ）^2｛｛１／（ｐ−ｑ）−１／（ｐ＋ｑ）｝^2＋｛１／（３ｐ−ｑ）−１／（３ｐ＋ｑ）｝^2＋｛１／（５ｐ−ｑ）−１／（５ｐ＋ｑ）｝^2＋・・・｝

＝４｛｛１／１−１／３｝^2＋｛１／５−１／７｝^2＋｛１／９−１／１１｝^2＋・・・｝

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