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＋・・・｝

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝