Ⅰ．Sine,cosine and logarithmie integral 1
Text-books and other tables 5
？(Cix) and ？(aix) 9
Ⅱ．Factorial function 9
ψ(x) 18
ψ＇(x) 18
Text-books and other tables 21
The incomplete factorial function 22
Ⅲ．Error integral and related functions 23
1．Error integral φ(x) 24
2．dn φ(x)/dxn 24
3．The functions of the parabolic cylinder 32
？ et2 dt 32
4．Fresnel＇s integrals 35
5．The after-effect function 38
Text-books and other tables 40
Ⅳ．Theta-functions 41
Modular function 43
Other tables 43
log q 49
Ⅴ．Elliptic Integrals 52
A．Incomplete Integrals 52
F(α,φ) 52
E(α,φ) 54
B．Complete Integrals 73
Integral of the third kind 81
Taxt-books and other tables 83
C．Inductance of coils 86
Ⅵ．Elliptic functions 90
Jacobian functions 90
Weicrstrass＇s functions 98
φ＇u,φu,ξu,σu for g2=0,g2=1 101
Text-books and other tables 106
Ⅶ．Legendre functions 107
Legendre＇s associated functions 110
Text-books and other tables 117
dPn/dθ 124
Ⅷ．Bessel funetions 126
1．Definitions 128
2．Asymptotic representations 137
3．Zeros 143
4．Elementary functional equations 144
5．Differential formulae 145
6．Integral formulae 145
7．Differential equations 146
8．Integral representations 147
a) Real argument． 154
Jn+0,5(x),J-n-ο,i(x) 154
Jο(x),J1(x) 156
Jο(x)=0;J1(x)=0 162
Text-books and other tables 164
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,．．．9 152
Jρ(n);n=1,2,．．．29 174
An(x)=n!/(x∶2)n Jn(x);n=0,1,2,．．．8 189
Nο(x),N1(x) 190
Roots of equations containing Bessel functions 204
9．The function ？ρ(z) of H．F．Weber and Lommel 210
10．The Struve function Qρ(x) 211
b) Imaginary argument． 224
Jο(ix),J1(ix) 224
Jn(ix);n=0,1,．．．11 224
J-ρ(x+iy)=0 230
Jn(ix)Jn(x)-iJn(x)J＇n(ix)=0,n=0,1,2 234
J n/3(i x);n=±1,±2 235
H(1)ο (ix),H(1)1 (ix) 242
c) Complex argument,especially x？i． 242
H(z)ξ (riz)=0 242
H(1)p (z)=0;H？(e)=0 243
Jο(x？i)=uο+ivο 244
？iJ1(x？i)=u1+iv1 244
H(1)ο (x？i)=Uο+iVο 250
？iH？(x？i)=U1+iV1 256
J(r？i)=biB 260
H(1)？(r？i)=hiη 259
Jο(r？i)∶J1(r？i) 264
H(1)ο(r？i)∶H(1)1(r？i) 265
Ⅸ．The Riemann Zeta-Function 269
Rernoulli＇s numbers 272
Zeros 0,5+iαn 274
Text-books and other tables 274
Ⅹ．Confiuent hypergeometric functions 275
Text-books and other tables 275
Ⅺ．Mathieu functions 283
Text-books and other tables 287
Some often used eonstants 295
Useful books for the computer 296
Index of tables of the elementary transcendentals 299
Supplementary Bibliography 302
General Index 305