《Tables of Functions With Formulae and Curves Fourth Edition》

Ⅰ．Sine,cosine and logarithmie integral1

Text-books and other tables5

？(Cix) and ？(aix)9

Ⅱ．Factorial function9

ψ(x)18

ψ＇(x)18

Text-books and other tables21

The incomplete factorial function22

Ⅲ．Error integral and related functions23

1．Error integral φ(x)24

2．dn φ(x)/dxn24

3．The functions of the parabolic cylinder32

？ et2 dt32

4．Fresnel＇s integrals35

5．The after-effect function38

Text-books and other tables40

Ⅳ．Theta-functions41

Modular function43

Other tables43

log q49

Ⅴ．Elliptic Integrals52

A．Incomplete Integrals52

F(α,φ)52

E(α,φ)54

B．Complete Integrals73

Integral of the third kind81

Taxt-books and other tables83

C．Inductance of coils86

Ⅵ．Elliptic functions90

Jacobian functions90

Weicrstrass＇s functions98

φ＇u,φu,ξu,σu for g2=0,g2=1101

Text-books and other tables106

Ⅶ．Legendre functions107

Legendre＇s associated functions110

Text-books and other tables117

dPn/dθ124

Ⅷ．Bessel funetions126

1．Definitions128

2．Asymptotic representations137

3．Zeros143

4．Elementary functional equations144

5．Differential formulae145

6．Integral formulae145

7．Differential equations146

8．Integral representations147

a)Real argument．154

Jn+0,5(x),J-n-ο,i(x)154

Jο(x),J1(x)156

Jο(x)=0;J1(x)=0162

Text-books and other tables164

J±0,25(x),J±0,75(x)164

1st and 2nd zero of Jρ(x)152

Jρ(xn)=0;p=0,1,2,．．．5;n=1,2,．．．9152

Jρ(n);n=1,2,．．．29174

An(x)=n!/(x∶2)n Jn(x);n=0,1,2,．．．8189

Nο(x),N1(x)190

Roots of equations containing Bessel functions204

9．The function ？ρ(z) of H．F．Weber and Lommel210

10．The Struve function Qρ(x)211

b)Imaginary argument．224

Jο(ix),J1(ix)224

Jn(ix);n=0,1,．．．11224

J-ρ(x+iy)=0230

Jn(ix)Jn(x)-iJn(x)J＇n(ix)=0,n=0,1,2234

J n/3(i x);n=±1,±2235

H(1)ο (ix),H(1)1 (ix)242

c)Complex argument,especially x？i．242

H(z)ξ (riz)=0242

H(1)p (z)=0;H？(e)=0243

Jο(x？i)=uο+ivο244

？iJ1(x？i)=u1+iv1244

H(1)ο (x？i)=Uο+iVο250

？iH？(x？i)=U1+iV1256

J(r？i)=biB260

H(1)？(r？i)=hiη259

Jο(r？i)∶J1(r？i)264

H(1)ο(r？i)∶H(1)1(r？i)265

Ⅸ．The Riemann Zeta-Function269

Rernoulli＇s numbers272

Zeros 0,5+iαn274

Text-books and other tables274

Ⅹ．Confiuent hypergeometric functions275

Text-books and other tables275

Ⅺ．Mathieu functions283

Text-books and other tables287

Some often used eonstants295

Useful books for the computer296

Index of tables of the elementary transcendentals299

Supplementary Bibliography302

General Index305