Integral Characteristics

• Integral type
  • Don't care Definite Indefinite
  • If definite
    Has a lower limit of Don't care -Infinity -1 0
    Has an upper limit of Don't care 0 1 Pi / 2 Pi 2 Pi Infinity
• Integrand
  • Contains specific numbers 2 3 4 5 6 7 8 9  
  • Contains indeterminates Don't care Yes No
  • Contains not-simple function arguments (e.g., f(2+3/x)) Don't care Yes No
  • Has a special form
    

    Laplace transform	Don't care	No	Yes
    Fourier transform	Don't care	No	Yes
    Mellin transform	Don't care	No	Yes
    Principal Value integral	Don't care	No	Yes

  • Powers
    

    Has a power	Don't care	No	Yes
    Has a square root	Don't care	No	Yes
    Has a square	Don't care	No	Yes
    Has a cube	Don't care	No	Yes

  • Contains following classes of functions
    

    Rational functions	Don't care	No	Yes
    Trigonometric functions	Don't care	No	Yes
    Inverse trigonometric functions	Don't care	No	Yes
    Hyperbolic functions	Don't care	No	Yes
    Inverse hyperbolic functions	Don't care	No	Yes
    Logarithm or Exponential functions	Don't care	No	Yes
    Bessel functions	Don't care	No	Yes

  • Contains following specific functions
    

    DLMF ref	Function	In Integrand			Name	LaTeX	Mathematica
    4.2.2	log(x)	Don't care	No	Yes	logarithm	\log{(x)}	Log[x]
    4.2.19	exp(x)	Don't care	No	Yes	exponential function	\exp{(x)}	Exp[x]
    4.14.1	sin(x)	Don't care	No	Yes	sine	\sin{(x)}	Sin[x]
    4.14.2	cos(x)	Don't care	No	Yes	cosine	\cos{(x)}	Cos[x]
    4.14.4	tan(x)	Don't care	No	Yes	tangent	\tan{(x)}	Tan[x]
    4.14.5	csc(x)	Don't care	No	Yes	cosecant	\csc{(x)}	in process
    4.14.6	sec(x)	Don't care	No	Yes	secant	\sec{(x)}	in process
    4.14.7	cot(x)	Don't care	No	Yes	cotangent	\cot{(x)}	in process
    4.28.1	sinh(x)	Don't care	No	Yes	hyperbolic sine	\sinh{(x)}	in process
    4.28.2	cosh(x)	Don't care	No	Yes	hyperbolic cosine	\cosh{(x)}	in process
    4.28.4	tanh(x)	Don't care	No	Yes	hyperbolic tangent	\tanh{(x)}	in process
    4.28.5	csch(x)	Don't care	No	Yes	hyperbolic cosecant	\csch{(x)}	in process
    4.28.6	sech(x)	Don't care	No	Yes	hyperbolic secant	\sech{(x)}	in process
    4.28.7	coth(x)	Don't care	No	Yes	hyperbolic cotangent	\coth{(x)}	in process
    5.2.1	Gamma(z)	Don't care	No	Yes	Gamma function	\FUNCTIONGamma{(z)}	in process
    5.2.2	Psi(z)	Don't care	No	Yes	related to Gamma function	\FUNCTIONPsi{(z)}	in process
    6.2.1	E_1(z)	Don't care	No	Yes	Exponential integral	in process	in process
    6.2.3	Ein(z)	Don't care	No	Yes	Exponential integral	in process	in process
    6.2.8	li(z)	Don't care	No	Yes	Logarithmic integral	in process	in process
    6.2.9	Si(z)	Don't care	No	Yes	Sine integral	in process	in process
    6.2.10	si(z)	Don't care	No	Yes	Sine integral	in process	in process
    6.2.11	Ci(z)	Don't care	No	Yes	Cosine integral	in process	in process
    6.2.12	Cin(z)	Don't care	No	Yes	Cosine integral	in process	in process
    6.2.15	Shi(z)	Don't care	No	Yes	Sinh integral	in process	in process
    6.2.16	Chi(z)	Don't care	No	Yes	Cosh integral	in process	in process
    7.2.1	erf(z)	Don't care	No	Yes	Error function	\erf{(z)}	in process
    7.2.2	erfc(z)	Don't care	No	Yes	Complementary error function	\erfc{(z)}	in process
    7.2.5	F(z)	Don't care	No	Yes	Dawson integral	\DawsonF{(z)}	in process
    7.2.6	[Script F](z)	Don't care	No	Yes	Fresnel Integral	in process	in process
    7.2.7	C(z)	Don't care	No	Yes	Fresnel Integral	\FresnelC{(z)}	in process
    7.2.8	S(z)	Don't care	No	Yes	Fresnel Integral	\FresnelS{(z)}	in process
    8.2.1	gamma(a,z)	Don't care	No	Yes	incomplete gamma function	\FUNCTIONgamma{(a,z)}	in process
    8.2.2	Gamma(a,z)	Don't care	No	Yes	incomplete gamma function	\FUNCTIONGammaTwoArg{(a,z)}	in process
    8.2.6	gamma^*(a,z)	Don't care	No	Yes	incomplete gamma function	\FUNCTIONgammaTwoArgStar{(a,z)}	in process
    9.2.3	Ai(z)	Don't care	No	Yes	Airy function	\Ai(z)	in process
    9.2.5	Bi(z)	Don't care	No	Yes	Bairy function	\Bi(z)	in process
    9.12.4	Gi(z)	Don't care	No	Yes	Scorer function	\Gi(z)	in process
    9.12.4	Hi(z)	Don't care	No	Yes	Scorer function	\Hi(z)	in process
    10.2.2	J_nu(z)	Don't care	No	Yes	Bessel function first kind	\BesselJ{\nu}{(z)}	in process
    10.2.3	Y_nu(z)	Don't care	No	Yes	Bessel function second kind (Weber function)	\BesselY{\nu}{(z)}	in process
    10.2.5	H_nu^1(z)	Don't care	No	Yes	Bessel function third kind (Hankel function)	\BesselHone{\nu}{(z)}	in process
    10.2.6	H_nu^2(z)	Don't care	No	Yes	Bessel function third kind (Hankel function)	\BesselHtwo{\nu}{(z)}	in process
    10.25.2	I_nu(z)	Don't care	No	Yes	Modified Bessel function	\BesselI{\nu}{(z)}	in process
    10.25.3	K_nu(z)	Don't care	No	Yes	Modified Bessel function	\BesselK{\nu}{(z)}	in process
    10.47.3	j_n(z)	Don't care	No	Yes	spherical Bessel function first kind	\Besselj{n}{(z)}	in process
    10.47.4	y_n(z)	Don't care	No	Yes	spherical Bessel function second kind	\Bessely{n}{(z)}	in process
    10.47.5	h_n^1(z)	Don't care	No	Yes	spherical Bessel function third kind	\Besselhone{n}{(z)}	in process
    10.47.6	h_n^2(z)	Don't care	No	Yes	spherical Bessel function third kind	\Besselhtwo{n}{(z)}	in process
    10.47.7	i_n^1(z)	Don't care	No	Yes	Modified spherical Bessel function	\Besselione{n}{(z)}	in process
    10.47.8	i_n^2(z)	Don't care	No	Yes	Modified spherical Bessel function	\Besselitwo{n}{(z)}	in process
    10.47.9	k_n(z)	Don't care	No	Yes	Modified spherical Bessel function	\Besselkone{n}{(z)}	in process
    10.61.1	ber_nu(x)	Don't care	No	Yes	Kelvin function	\Kelvinber{\nu}{(x)}	in process
    10.61.1	bei_nu(x)	Don't care	No	Yes	Kelvin function	\Kelvinbei{\nu}{(x)}	in process
    10.61.2	ker_nu(x)	Don't care	No	Yes	Kelvin function	\Kelvinker{\nu}{(x)}	in process
    10.61.2	kei_nu(x)	Don't care	No	Yes	Kelvin function	\Kelvinkei{\nu}{(x)}	in process
    11.2.1	H_nu(z)	Don't care	No	Yes	Struve Function	\StruveH{\nu}{(z)}	in process
    11.2.2	L_nu(z)	Don't care	No	Yes	Struve Function	\StruveL{\nu}{(z)}	in process
    11.2.5	K_nu(z)	Don't care	No	Yes	Struve Function	\StruveK{\nu}{(z)}	in process
    11.2.6	M_nu(z)	Don't care	No	Yes	Struve Function	\StruveM{\nu}{(z)}	in process
    12.2.1	U(a,z)	Don't care	No	Yes	Parabolic Cylinder Function	\ParabolicCylinderFunctionU{(a,z)}	in process
    12.2.1	V(a,z)	Don't care	No	Yes	Parabolic Cylinder Function	\ParabolicCylinderFunctionV{(a,z)}	in process
    12.2.3	W(a,z)	Don't care	No	Yes	Parabolic Cylinder Function	\ParabolicCylinderFunctionW{(a,z)}	in process
    12.2.4	D_nu(z)	Don't care	No	Yes	Parabolic Cylinder Function	\ParabolicCylinderFunctionD{nu}{(z)}	in process
    13.2.1	M(a,b,z)	Don't care	No	Yes	Kummer Function	\KummerM{(a,b,z)}	in process
    13.2.6	U(a,b,z)	Don't care	No	Yes	Kummer Function	\KummerU{(a,b,z)}	in process

  Entry Characteristics
  has constraints
  has transformation
  has a link to a proof
  has references
  has LaTeX representation
  has Mathematica representation
  
  Contributor Characteristics
  • Was first created by Don't care Dan John Unknown
    
  • Was updated by Don't care Dan John Unknown
    
  • Was last updated by Don't care Dan John Unknown

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