Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8cm)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8cm.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 21/4}, z] == (-4 (-3845501485056000 + 2437263844178625 Sqrt[z] - 6272509027900500 z + 1449320317830000 z^(3/2) - 3982778423870400 z^2 + 639410334393600 z^(5/2) - 1944608916096000 z^3 + 419138108928000 z^(7/2) - 1927510102425600 z^4 - 97304966922240 z^(9/2) + 402288904765440 z^5 + 4574816501760 z^(11/2) - 18495056117760 z^6 - 66186117120 z^(13/2) + 265549774848 z^7 + 268435456 z^(15/2) - 1073741824 z^8 + E^(4 Sqrt[z]) (3845501485056000 + 2437263844178625 Sqrt[z] + 6272509027900500 z + 1449320317830000 z^(3/2) + 3982778423870400 z^2 + 639410334393600 z^(5/2) + 1944608916096000 z^3 + 419138108928000 z^(7/2) + 1927510102425600 z^4 - 97304966922240 z^(9/2) - 402288904765440 z^5 + 4574816501760 z^(11/2) + 18495056117760 z^6 - 66186117120 z^(13/2) - 265549774848 z^7 + 268435456 z^(15/2) + 1073741824 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (10128266814290625 + 19944894649680000 z + 13789062967680000 z^2 + 6788461768704000 z^3 + 7986425610240000 z^4 - 1622638854144000 z^5 + 74177776189440 z^6 - 1063004405760 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (10128266814290625 + 19944894649680000 z + 13789062967680000 z^2 + 6788461768704000 z^3 + 7986425610240000 z^4 - 1622638854144000 z^5 + 74177776189440 z^6 - 1063004405760 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(23017588732723200 z^(9/2))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]