An Atlas of Functions

Table of Contents

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   Book Overview
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   Chapter 1 General Considerations
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   Chapter 2 The Constant Function c
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   Chapter 3 The Factorial Function n !
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   Chapter 4 The Zeta Numbers and Related Functions
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   Chapter 5 The Bernoulli Numbers B n
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   Chapter 6 The Euler Numbers E n
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   Chapter 7 The Binomial Coefficients $\left( {_m^v } \right)$
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   Chapter 8 The Linear Function bx + c and Its Reciprocal
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    Chapter 9 Modifying Functions
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    Chapter 10 The Heaviside u( x − a ) And Dirac δ( x − a ) Functions
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    Chapter 11 The Integer Powers x n And ( bx + c ) n
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    Chapter 12 The Square-Root Function $\sqrt {bx + c}$ and Its Reciprocal
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    Chapter 13 The Noninteger Powers x v
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    Chapter 14 The Semielliptic Function $\left( {b/a} \right)\sqrt {a^2 {\kern 1pt} - x^2 }$ and Its Reciprocal
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    Chapter 15 The Semihyperbolic Functions $\left( {b/a} \right)\sqrt {x^2 {\kern 1pt} \pm a^2 }$ And Their Reciprocals
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    Chapter 16 The Quadratic Function ax 2 + bx + c and Its Reciprocal
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    Chapter 17 The Cubic Function x 3 + ax 2 + bx + c
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    Chapter 18 Polynomial Functions
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    Chapter 19 The Pochhammer Polynomials ( x ) n
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    Chapter 20 The Bernoulli Polynomials B n ( x )
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    Chapter 21 The Euler Polynomials E n ( x )
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    Chapter 22 The Legendre Polynomials P n ( x )
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    Chapter 23 The Chebyshev Polynomials T n ( x ) and U n ( x )
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    Chapter 24 The Laguerre Polynomials L n ( x )
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    Chapter 25 The Hermite Polynomials H n ( x )
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    Chapter 26 The Logarithmic Function ln( x )
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    Chapter 27 The Exponential Function exp(± x )
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    Chapter 28 Exponentials of Powers exp(± x v )
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    Chapter 29 The Hyperbolic Cosine Cosh( x ) and Sine Sinh( x ) Functions
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    Chapter 30 The Hyperbolic Secant Sech( x ) and Cosecant Csch( x ) Functions
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    Chapter 31 The Hyperbolic Tangent tanh( x ) and Cotangent coth( x ) Functions
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    Chapter 32 The Inverse Hyperbolic Functions
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    Chapter 33 The Cosine cos( x ) and Sine sin( x ) Functions
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    Chapter 34 The Secant sec( x ) And cosecant csc( x ) Functions
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    Chapter 35 The Tangent tan( x ) and Cotangent cot( x ) Functions
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    Chapter 36 The Inverse Circular Functions
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    Chapter 37 Periodic Functions
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    Chapter 38 The Exponential Integrals Ei( x ) and Ein( x )
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    Chapter 39 Sine and Cosine Integrals
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    Chapter 40 The Fresnel Integrals C( x ) and S( x )
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    Chapter 41 The Error Function erf( x ) and Its Complement erfc( x )
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    Chapter 42 The $\exp \left( x \right){\mathop{\rm erfc}\nolimits} \left( {\sqrt x } \right)$ and Related Functions
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    Chapter 43 Dawson’s Integral daw( x )
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    Chapter 44 The Gamma Function Γ( v )
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    Chapter 45 The Digamma Function ψ( v )
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    Chapter 46 The Incomplete Gamma Functions
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    Chapter 47 The Parabolic Cylinder Function D v ( x )
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    Chapter 48 The Kummer Function M( a , c , x )
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    Chapter 49 The Tricomi Function U( a , c , x )
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    Chapter 50 The Modified Bessel Functions I n ( x ) of Integer Order
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    Chapter 51 The Modified Bessel Function I v ( x ) of Arbitrary Order
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    Chapter 52 The Macdonald Function K v ( x )
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    Chapter 53 The Bessel Functions J n ( x ) of Integer Order
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    Chapter 54 The Bessel Function J v ( x ) of Arbitrary Order
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    Chapter 55 The Neumann Function Y v ( x )
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    Chapter 56 The Kelvin Functions
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    Chapter 57 The Airy Functions Ai( x ) and Bi( x )
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    Chapter 58 The Struve Function h v ( x )
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    Chapter 59 The Incomplete Beta Function B( v ,μ, x )
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    Chapter 60 The Legendre Functions P v ( x ) and Q v ( x )
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    Chapter 61 The Gauss Hypergeometric Function F( a , b , c , x )
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    Chapter 62 The Complete Elliptic Integrals K( k ) and E( k )
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    Chapter 63 The Incomplete Elliptic Integrals F( k ,ϕ) AND E( k ,ϕ)
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    Chapter 64 The Jacobian Elliptic Functions
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    Chapter 65 The Hurwitz Function ζ( v , u )