x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...

2025年1月31日 · The "imaginary error function" erfi (z) is an entire function defined by erfi (z)=-ierf (iz), (1) where erf (z) is the erf function. It is implemented in the Wolfram Language as Erfi [z]. …

Compute the imaginary error function for the same numbers converted to symbolic objects. For most symbolic (exact) numbers, erfi returns unresolved symbolic calls. Use vpa to …

Mathematical function, suitable for both symbolic and numerical manipulation. For certain special arguments, Erfi automatically evaluates to exact values. Erfi can be evaluated to arbitrary numerical precision.

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ERFI Imaginary Error Function ERFI.1 Introduction Let x be a complex variable of C\{∞}.The function Imaginary Error Function (noted erfi) is defined by the following second order differential equation −2x ∂y(x) ∂x + ∂2y(x) ∂x2 (ERFI.1.1) = 0. The initial conditions of ERFI.1.1 are given at 0 by erfi(0) = 0, ∂erfi(x) ∂x (0 ...

Instead of using definite integrals, the three univariate error functions can be defined through the following infinite series. Here is a quick look at the graphics for the probability integrals and inverses along the real axis.

Erfi[z] (246 formulas) Primary definition (1 formula) Specific values (6 formulas) General characteristics (6 formulas) Series representations (17 formulas) Integral representations (5 formulas) Continued fraction representations (10 formulas) Differential equations (11 formulas) Transformations (5 formulas) Complex characteristics (10 formulas)

The probability integrals , , and are entire functions with an essential singular point at , and they do not have branch cuts or branch points. The generalized error function is an analytical function of and , which is defined in . For fixed , it is an entire function of . For fixed , it is an entire function of . It does not have branch cuts ...

2024年10月6日 · Calculation Example: The Erfi function, also known as the imaginary error function, is a special function that arises in various branches of science, including probability, statistics, and physics. It is defined as the integral of the Gaussian function e^(t^2) from 0 to x, scaled by a factor of 2/√π.