# Cheat Sheet

Cheat Sheet

Polylogarithm Function
• (this function is defined in complex plane over a disk with radius 1)

Some formulas for argument ½ with small n are known:

Zeta Riemann Function (Euler’s Zeta Function)

General Zeta Riemann Function

Dirichlet Eta Function

Relationship between Zeta and Eta Functions

Zeta and Gamma Function

Gamma Function

Beta Function

• ,

Digamma Function

Euler Product

Riemann Hypothesis
Riemann conjectured that all zeros of in the critical strip line on the critical line Re s = ½.

Series Power of Natures Numbers

Arithmetic

Geometric

Binomial
• , where
•

Maclaurin Series
•

Taylor Series
• , where
•

Some Power Series

Trigonometry

Law of Sines

Law of Cosines

Hyperbolic functions

Complex

Half Angle Tangent

Multiple Angle Identities for Cosine
•  (Double angle identity for cosine)
•  (Triple angle cosine identity for cosine)
•  (Quintuple angle cosine identity)
•  (Sextuple angle cosine identity)
• (Septic angle cosine Identity)
Multiple Angle Identities for Hyperbolic Cosine
•  (Double angle identity for hyperbolic cosine)
•  (Triple angle cosine identity for hyperbolic cosine)
•  (Quadruple angle identity hyperbolic cosine)
•  (Quintuple angle identity for hyperbolic cosine)
•  (Sextuple angle identity for hyperbolic cosine)
• (Septic angle identity for hyperbolic cosine)

Multiple Angle Identities for Tangent

•  (Double angle identity for tangent)
•  (Triple angle identity for tangent)
•  (Quadruple angle identity for tangent)
•  (Quintuple angle identity for tangent)
•  (Sextuple angle identity for tangent)
•  (Septic angle Identity for tangent)

Multiple Angle Identities for Hyperbolic Tangent

•  (Double angle identity for hyperbolic tangent)
•  (Triple angle identity for hyperbolic tangent)
•  (Quadruple angle identity for hyperbolic tangent)
•  (Quintuple angle identity for hyperbolic tangent)
•  (Sextuple angle identity for hyperbolic tangent)
•  (Septic angle Identity for hyperbolic tangent)