Formula:236

Digital Library of Mathematical Functions ID 1.8.E12

${\displaystyle{\displaystyle\int^{x}_{0}(f(t)-\tfrac{1}{2}a_{0})\mathrm{d}t=\sum^{\infty}_{n=1}\frac{a_{n}\sin\left(nx\right)+b_{n}(1-\cos\left(nx\right))}{n},}}$

Constraint(s)

${\displaystyle{\displaystyle 0\leq x\leq 2\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

Resources that cite this formula

No records found.