接近整数
其他例子

| 0 | 1 | 2 | 3 |
| --- | --- | --- | --- |
|  {}_{\cos \left\{\pi \cos \left[\pi \cos \ln \left(\pi +20\right)\right]\right\}\approx -0.9999999999999999999999999999999999606783} |  {}_{\sin 2017{\sqrt[{5}]{2}}\approx -0.9999999999999999785} |  {}_{\sum _{k=1}^{\infty }{\frac {\lfloor n\tanh \pi \rfloor }{10^{n}}}-{\frac {1}{81}}\approx 1.11\times 10^{-269}} |  {}_{{\sqrt {29}}\left(\cos {\frac {2\pi }{59}}-\cos {\frac {24\pi }{59}}\right)-{\frac {19}{5}}\approx 3.057684294154\times 10^{-6}} |
|  {}_{1+{\frac {103378831900730205293632}{e^{3\pi {\sqrt {163}}}}}-{\frac {196884}{e^{2\pi {\sqrt {163}}}}}-{\frac {262537412640768744}{e^{\pi {\sqrt {163}}}}}\approx 1.161367900476\times 10^{-59}} |  {}_{{\frac {\ln ^{2}262537412640768744}{\pi ^{2}}}-163\approx 2.32167\times 10^{-29}} |  {}_{10\tanh {\frac {28}{15}}\pi -{\frac {\pi ^{9}}{e^{8}}}\approx 3.661398\times 10^{-8}} |  {}_{{\sqrt[{4}]{\frac {91}{10}}}-{\frac {33}{19}}\approx 3.661398\times 10^{-8}} |
|  {}_{\gamma -{10 \over 81}\left(11-2{\sqrt {10}}\right)=\int _{0}^{\infty }\left({\frac {1}{e^{x}-1}}-{\frac {1}{xe^{x}}}\right){\rm {d}}x-{10 \over 81}\left(11-2{\sqrt {10}}\right)\approx 2.72\times 10^{-7}} |  {}_{{\frac {\left(5+{\sqrt {5}}\right)\Gamma \left({3 \over 4}\right)}{e^{{\frac {5}{6}}\pi }}}\approx 1.000000000000045422} |  {}_{{1 \over 4}\left(\cos {1 \over 10}+\cosh {1 \over 10}+2\cos {{\sqrt {2}} \over 20}\cosh {{\sqrt {2}} \over 20}\right)\approx 1.000000000000248} |  {}_{e^{6}-\pi ^{5}-\pi ^{4}\approx 1.7673\times 10^{-5}} |
|  {}_{{\sqrt {29}}\left(\cos {\frac {2\pi }{59}}-\cos {\frac {24\pi }{59}}\right)\approx 3.0576842941540143382\times 10^{-6}} |  {}_{\left(3{\sqrt {5}}\right)^{\gamma }=\left(3{\sqrt {5}}\right)^{\int _{0}^{\infty }\left({\frac {1}{e^{x}-1}}-{\frac {1}{xe^{x}}}\right){\rm {d}}x}\approx 3.000060964} |  {}_{e^{\phi _{0}\left({\frac {2+{\sqrt {3}}}{4}}\right)}=e^{\int _{0}^{\infty }\left({\frac {1}{te^{t}}}-{\frac {e^{{\frac {2-{\sqrt {3}}}{4}}t}}{e^{t}-1}}\right){\rm {d}}t}\approx 1.99999969} |  {}_{{\frac {\sqrt[{3}]{9}}{3\ln 2}}\approx 1.00030887} |
|  {}_{\sum _{k=-\infty }^{\infty }10^{-{\frac {k^{2}}{10000}}}-100{\sqrt {\frac {\pi }{\ln 10}}}=\theta _{3}\left(0,{\frac {1}{\sqrt[{10000}]{10}}}\right)-100{\sqrt {\frac {\pi }{\ln 10}}}\approx 1.3809\times 10^{-18613}} |  {}_{{\pi ^{9} \over e^{8}}\approx 9.998387} |  {}_{e^{\pi }-\pi \approx 19.999099979} |  {}_{{\frac {e^{\pi }-\ln 3}{\ln 2}}-{\frac {4}{5}}\approx 31.0000000033} |
|  {}_{{\frac {\pi ^{11}}{e^{3}}}-\Gamma \left[\Gamma \left(\pi +1\right)+1\right]={\frac {\pi ^{11}}{e^{3}}}-\int _{0}^{\infty }{\frac {t^{\int _{0}^{\infty }{\frac {u^{\pi }}{e^{u}}}{\rm {d}}u}}{e^{t}}}{\rm {d}}t\approx 7266.9999993632596} |  {}_{163\left(\pi -e\right)\approx 68.999664} |  {}_{\left({\frac {23}{9}}\right)^{5}={\frac {6436343}{59049}}\approx 109.00003387} |  {}_{88\ln 89\approx 395.00000053} |
|  {}_{510\lg 7\approx 431.00000040727098} |  {}_{272\log _{\pi }97\approx 1087.000000204} |  {}_{{\frac {53453}{\ln 53453}}\approx 4910.00000122} |  {}_{{\frac {53453}{\ln 53453}}+{\frac {163}{\ln 163}}\approx 4941.99999995925082} |
|  {}_{{\sqrt[{8}]{{\frac {\sqrt {2}}{4}}\left(\pi ^{17}-4e^{2\pi }+4\pi e^{\pi }\right)}}-{\sqrt[{8}]{{\frac {\sqrt {2}}{4}}\left(\pi ^{17}-4e^{2\pi }-4\pi e^{\pi }\right)}}\approx 2.570287024592328869357\times 10^{-6}} |  {}_{10-{\sqrt[{8}]{{\frac {\sqrt {2}}{4}}\left(\pi ^{17}-4e^{2\pi }-4\pi e^{\pi }\right)}}\approx 2.57055302118\times 10^{-6}} |  {}_{10-{\sqrt[{8}]{{\frac {\sqrt {2}}{4}}\left(\pi ^{17}-4e^{2\pi }+4\pi e^{\pi }\right)}}\approx 2.65996596963\times 10^{-10}} |  {}_{{\frac {163}{\ln 163}}\approx 31.9999987343} |
\sin 11=-0.999990207...，這是由於 3.5\pi \approx 10.9956\approx 11的緣故，另一個類似的例子為 \sin 355=-0.00003014435335948844921433...
{\sqrt {1^{2}+2^{2}+3^{2}+4^{2}+.......+552057^{2}}}\approx 236818619.0000004307
{\frac {5^{6}}{6^{5}}}\approx 2