Integrals Related to the Error Function 1st Edition by Nikolai Korotkov, Alexander Korotkov ISBN 978-0367408206 0367408201

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Product details: 

ISBN 10:   0367408201

ISBN 13: 978-0367408206

Author: Nikolai E. Korotkov, Alexander N. Korotkov 

Integrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration).

Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals.

Features

The first book in English language to present a comprehensive collection of integrals related to the error function
Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.

Table of contents: 

PART 1

Indefinite Integrals

1.1 INTEGRALS OF THE FORM ∫z” exp[ = (az+B)²]dz

1.2 INTEGRALS OF THE FORM [z” exp(a²z² +ẞz+y)dz

1.3 INTEGRALS OF THE FORM

ſerf” (az + B)exp[-(az+b)²] dz

1.4 INTEGRALS OF THE FORM

[z” erf (az+B)exp[-(az+β)²]dz

1.5 INTEGRALS OF THE FORM ∫z” erf (az+B)exp(β₁z+y)dz

1.6 INTEGRALS OF THE FORM

[z2m+1 erf (az +ẞ)exp(a²z² + y)dz

1.7 INTEGRALS OF THE FORM

[z2m+1 erf (az +ẞ)exp(a₁z² + y)dz α Z

1.8 INTEGRALS OF THE FORM [z” erf² (az) exp(a²z²)dz

1.9 INTEGRALS OF THE FORM [z” erf (az+B)dz

1.10 INTEGRALS OF THE FORM [z” erf² (az +ẞ)dz

1.11 INTEGRALS OF THE FORM 22 erf (az)erf (az)dz

1.12 INTEGRALS OF THE FORM 22m+ erf³ (az)dz

1.13 INTEGRALS OF THE FORMS

[z”sin” (a²z² +ẞz+y) dz,

[zº sinh” (a²z²+ẞz+y)dz,

[z cos (a²z²+ẞz+y)dz,

[zº cosh (a²z² +ẞz+y)dz

1.14 INTEGRALS OF THE FORM

[z” sin(a²z²+ẞz+y)exp(ẞ,z)dz

1.15 INTEGRALS OF THE FORM

[z” exp(-a2z²+ẞz)sin(β₁z+y)dz

1.16 INTEGRALS OF THE FORM

[z”exp(-az²+ẞz)sin(a,z²+B₁z+y)dz

1.17 INTEGRALS OF THE FORM

Jzerf (az+ẞ)exp(ẞız)sin(ẞaz+y)dz

1.18 INTEGRALS OF THE FORM

[22 erf (az+ẞ) exp(a,z²)sin(azz²+y)dz

PART 2 Definite Integrals

2.1 INTEGRALS OF z” exp[7(az+β)²]

2.2 INTEGRALS OF 2º exp(a²z² + β2+y)

2.3 INTEGRALS OF erf” (az +ẞ)exp[-(az+B)²]

2.4 INTEGRALS OF z” erf (az + β)exp[-(az+b)²]

2.5 INTEGRALS OF 2″ erf (az+ẞ)exp(ẞız + γ)

2.6 INTEGRALS OF 2m+¹ erf (az+ẞ)exp(-az²)

2.7 INTEGRALS OF 2″ exp(-az²+ẞz)erí (a,z+βι), z” exp(-az²) erf (a,z+β₁) erf (a2z+ẞ2)

2.8 INTEGRALS OF sin²+(a²z²+ẞz+y),

sinh(a²z²+ẞz+y), cos(a²z² +ẞz+y), cosh²+(a²z² +ẞz+y)

2.9 INTEGRALS OF 7″ sin (a²z² +ẞz+y) exp (ẞ,z)

2.10 INTEGRALS OF

z” exp(-az²+ẞz)sin(a,z² + β₁z+y)

2.11 INTEGRALS OF z” ref (az +β)exp(ẞız)sin(ẞ22+y)

2.12 INTEGRALS OF

220+ erf (az +ẞ)exp(-az²)sin(az²+7)

2.13 INTEGRALS OF

z” erf (az +ẞ)exp(-a,z² +ẞ,z)sin(azz² + B₂z+y), z” erf (az)exp(-az²)sin(ẞz), z” erf (az)exp(-az²)cos(ẞz)

2.14 INTEGRALS OF z” [±1-erf (az+β)],

z” [erf (aiz+ẞ1) 7erf (a2z+B2)]

2.15 INTEGRALS OF z” [±1-erf(az+β)],

z” [1-erf² (az+B)], z” [erf (aiz+ẞi) 7erf² (a2z+β2)], z” [erf² (az+B₁)-erf² (a2z+B2)]

2.16 INTEGRALS OF z” exp(Bz)[±1-erf (az+βι)],

z” exp(ẞz)[erf (a₁z+β₁)+erf (a2z+B2)]

2.17 INTEGRALS OF

z” exp(-a²z²+ẞz) [±1-erf(az+β₁)],

z” exp(-a²z²+ẞz) [erf (a₁z+B₁)+erf (a2z+B2)]

2.18 INTEGRALS OF z” erf (az+Bi)exp[-(a2z+B2)²],

z[±1-erf(az+Bi)] exp[-(α+β2)²], z” exp(ẞz) erf² (az+βι), z” exp(Bz)[1-erf² (az+βι)],

z” exp(ẞz)[erf² (az+B₁)-erf² (a2z+B2)]

2.19 INTEGRALS OF

[(±1)” -erf” (az+B)] exp[-(α+β)²], 22m+[1-erf(az)],22m+[±1-erf³ (az)], z2m+[erf³ (az) erf³ (az)], 22 erf² (az)exp(-az²), Z 22 [1-erf² (az)]exp(-az²) 200 Z

2.20 INTEGRALS OF zsin(ẞz+y)[±1-erf (az+B)],

z” sin (β2+7)[erf (az+β₁)+erí (a2z+β2)], z” sin(az2 +ẞz+y)[±1-erf (az+β₁)], z” sin(az2+ẞz+y)[erf (a,z+ẞ₁)+erf (a2z+B2)]

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Tags: Nikolai Korotkov, Alexander Korotkov, Integrals Related, Error Function