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Error and complementary error functions. Exponential integral. Sine and cosine integrals. Fresnel sine and cosine integrals.

Error function

Miscellaneous

4)        erf (-x) = - erf(x)

5)        erf (0) = 0

6)        erf (∞) = 1

Complementary Error function

Miscellaneous

10)      erfc (0) = 1

11)      erfc (∞) = 0

Exponential integral

Miscellaneous

16)      Ei(∞) = 0

where γ is Euler’s constant.

Sine integral

Miscellaneous

20)      Si(-x) = - Si(x)

21)      Si(0) = 0

22)      Si(∞) = π/2

Cosine integral

Miscellaneous

26)      Ci(∞) = 0

where γ is Euler’s constant.

Fresnel sine integral

Miscellaneous

30)      S(-x) = - S(x)

31)      S(0) = 0

32)      S(∞) = 1/2

Fresnel cosine integral

Miscellaneous

36)      C(-x) = - C(x)

31)      C(0) = 0

32)      C(∞) = 1/2

Source: Spiegel. Mathematical Handbook of Formulas and Tables. (Schaum)

References.

1. Spiegel. Mathematical Handbook of Formulas and Tables. (Schaum)