Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab3c)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ab3c.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(9/2), 23/4}, z] == (209 (4 z^(1/4) (-42706082293875 - 56941443058500 Sqrt[z] - 39397322764800 z - 17822598393600 z^(3/2) - 5545497484800 z^2 - 1178353612800 z^(5/2) - 162897100800 z^3 - 12517048320 z^(7/2) - 580321280 z^4 + 173801472 z^(9/2) + E^(4 Sqrt[z]) (42706082293875 - 56941443058500 Sqrt[z] + 39397322764800 z - 17822598393600 z^(3/2) + 5545497484800 z^2 - 1178353612800 z^(5/2) + 162897100800 z^3 - 12517048320 z^(7/2) + 580321280 z^4 + 173801472 z^(9/2))) + 663 E^(2 Sqrt[z]) Sqrt[2 Pi] (64413397125 - 9284814000 z + 818496000 z^2 - 64512000 z^3 + 6881280 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - 663 E^(2 Sqrt[z]) Sqrt[2 Pi] (64413397125 - 9284814000 z + 818496000 z^2 - 64512000 z^3 + 6881280 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(1649267441664 z^(19/4))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule 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]