Titanium hydroxide, photocatalyst, and coating agent

A titanium hydroxide having

• (i) a primary differential spectrum of radial structure function obtained from an extended X-ray absorption fine structure spectrum of titanium K absorption edge, the primary differential spectrum having two or more maximal intensities and two or more minimal intensities at interatomic distances in the range of from 1.4 Å to 2.8 Å, at least two maximal intensities being at an interatomic distance of from 1.4 Å to 1.7 Å and at an interatomic distance of from 2.2 Å to 2.5 Å, respectively, and at least two minimal intensities being at an interatomic distance of from 1.9 Å to 2.2 Å and at the interatomic distance of from 2.5 Å to 2.8 Å, respectively;
• and
• (ii) index X calculated by the equation:
• X=(U2−L2)/(U1−L1)
• of about 0.06 or more, wherein U1 and U2 represent the maximal-intensity values at the interatomic distance of from 1.4 Å to 1.7 Å and at the interatomic distance of from 2.2 Å to 2.5 Å, respectively, and L1 and L2 represent the minimal-intensity values at the interatomic distance of from 1.9 Å to 2.2 Å and at the interatomic distance of from 2.5 Å to 2.8 Å, respectively, of the primary differential spectrum.