Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 35

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 35

Published $\text {1968}$

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$35 \quad$ Miscellaneous Special Functions

Error Function $\ds \map \erf x = \frac 2 {\sqrt \pi} \int_0^x e^{-u^2} \rd u$

$35.1$: Power Series Expansion for Error Function

$35.2$: Asymptotic Expansion for Error Function

$35.3$: Properties of Error Function

$35.3.1$: Error Function is Odd

$35.3.2$: Error Function of Zero

$35.3.3$: Limit to Infinity of Error Function

Complementary Error Function $\map \erfc x = 1 - \map \erf x$

$35.4$: Power Series Expansion for Complementary Error Function

$35.5$: Asymptotic Expansion for Complementary Error Function

$35.6$: Properties of Complementary Error Function

$35.6.1$: Complementary Error Function of Zero

$35.6.2$: Limit to Infinity of Complementary Error Function

Exponential Integral $\ds \map \Ei x = \int_x^\infty \frac {e^{-t} } t \rd t$

$35.7$: Characterization of Exponential Integral Function

$35.8$: Power Series Expansion for Exponential Integral Function

$35.9$: Asymptotic Expansion for Exponential Integral Function

$35.10$: Limit to Infinity of Exponential Integral Function

Sine Integral $\ds \map \Si x = \int_0^x \frac {\sin u} u \rd u$

$35.11$: Power Series Expansion for Sine Integral Function

$35.12$: Asymptotic Expansion for Sine Integral Function

$35.13$: Properties of Sine Integral Function

$35.13.1$: Sine Integral Function is Odd

$35.13.2$: Sine Integral Function of Zero

$35.13.3$: Limit to Infinity of Sine Integral Function

Cosine Integral $\ds \map \Ci x = \int_x^\infty \frac {\cos u} u \rd u$

$35.14$: Characterization of Cosine Integral Function

$35.15$: Power Series Expansion for Cosine Integral Function plus Logarithm

$35.16$: Asymptotic Expansion for Cosine Integral Function

$35.17$: Limit to Infinity of Cosine Integral Function

Fresnel Sine Integral $\ds \map {\mathrm S} x = \sqrt {\frac 2 \pi} \int_0^x \sin u^2 \rd u$

$35.18$: Power Series Expansion for Fresnel Sine Integral Function

$35.19$: Asymptotic Expansion for Fresnel Sine Integral Function

$35.20$: Properties of Fresnel Sine Integral Function

$35.20.1$: Fresnel Sine Integral Function is Odd

$35.20.2$: Fresnel Sine Integral Function of Zero

$35.20.3$: Limit to Infinity of Fresnel Sine Integral Function

Fresnel Cosine Integral $\ds \map {\mathrm C} x = \sqrt {\frac 2 \pi} \int_0^x \cos u^2 \rd u$

$35.21$: Power Series Expansion for Fresnel Cosine Integral Function

$35.22$: Asymptotic Expansion for Fresnel Cosine Integral Function

$35.23$: Properties of Fresnel Cosine Integral Function

$35.23.1$: Fresnel Cosine Integral Function is Odd

$35.23.2$: Fresnel Cosine Integral Function of Zero

$35.23.3$: Limit to Infinity of Fresnel Cosine Integral Function

Riemann Zeta Function $\ds \map \zeta x = \frac 1 {1^x} + \frac 1 {2^x} + \frac 1 {3^x} + \ldots$

$35.24$: Integral Representation of Riemann Zeta Function in terms of Gamma Function

$35.25$: Functional Equation for Riemann Zeta Function

$35.26$: Riemann Zeta Function at Even Integers

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