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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)
  •  (Quadruple angle cosine identity)
  •  (Quintuple angle cosine identity)
  •  (Sextuple angle cosine identity)
  • (Septic angle cosine Identity)

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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)

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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)

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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)

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