Integrals of zero-order Bessel functions

Integrals of zero-order Bessel functions#

Integral of \(I_0\)#

math53.bessel_i0_int(x)#

Returns the integral \(\displaystyle \int_0^x I_0(t) \mathrm{d}t.\) See also Wikipedia [1370], MathWorld [980], NIST [468], BoostMath [114], Ehrhardt [309] (3.1.5.1).

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.BesselI0Int(0.5)
xreal('5.2359877559829887307E-1')
>>> xreal.BesselI0Int('0.51')
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.BesselI0Int(0.5)
Gpr('5.2359877559829887307E-1')
>>> Gpr.BesselI0Int('0.51')
Gpr('5.3518479027559984754E-1')

Integral of \(J_0\)#

math53.bessel_j0_int(x)#

Returns the integral \(\displaystyle \int_0^x J_0(t) \mathrm{d}t.\) See also Wikipedia [1356], MathWorld [951], NIST [463], BoostMath [100], Ehrhardt [309] (3.1.5.2).

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.BesselJ0Int(0.5)
xreal('5.2359877559829887307E-1')
>>> xreal.BesselJ0Int('0.51')
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.BesselJ0Int(0.5)
Gpr('5.2359877559829887307E-1')
>>> Gpr.BesselJ0Int('0.51')
Gpr('5.3518479027559984754E-1')

Integral of \(K_0\)#

math53.bessel_k0_int(x)#

Returns the integral \(\displaystyle \int_0^x K_0(t) \mathrm{d}t, \quad x \ge 0.\) See also Wikipedia [1370], MathWorld [981], NIST [469], BoostMath [114], Ehrhardt [309] (3.1.5.3).

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.BesselK0Int(0.5)
xreal('5.2359877559829887307E-1')
>>> xreal.BesselK0Int('0.51')
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.BesselK0Int(0.5)
Gpr('5.2359877559829887307E-1')
>>> Gpr.BesselK0Int('0.51')
Gpr('5.3518479027559984754E-1')

Integral of \(Y_0\)#

math53.bessel_y0_int(x)#

Returns the integral \(\displaystyle \int_0^x Y_0(t) \mathrm{d}t, \quad x \ge 0.\) See also Wikipedia [1357], MathWorld [952], NIST [464], BoostMath [100], Ehrhardt [309] (3.1.5.4).

An example in Python

>>> from xlcalcnet import xreal
>>> xreal.BesselY0Int(0.5)
xreal('5.2359877559829887307E-1')
>>> xreal.BesselY0Int('0.51')
xreal('5.3518479027559984754E-1')

An example in Visual Basic

>>> from xlcalcnet import Gpr
>>> Gpr.BesselY0Int(0.5)
Gpr('5.2359877559829887307E-1')
>>> Gpr.BesselY0Int('0.51')
Gpr('5.3518479027559984754E-1')
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