Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9864)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.9864.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(5/2), 23/4}, z] == -((209 (4 z^(1/4) (15652775985721875 + 20870367980962500 Sqrt[z] + 11514685782600000 z + 2631928178880000 z^(3/2) - 80818804684800 z^2 - 8507242598400 z^(5/2) + 50781694279680 z^3 - 57238473277440 z^(7/2) + 16834845081600 z^4 - 47692720373760 z^(9/2) + 3316415201280 z^5 - 10970386661376 z^(11/2) + 500095254528 z^6 - 1687116840960 z^(13/2) + 119185342464 z^7 - 489626271744 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-15652775985721875 + 20870367980962500 Sqrt[z] - 11514685782600000 z + 2631928178880000 z^(3/2) + 80818804684800 z^2 - 8507242598400 z^(5/2) - 50781694279680 z^3 - 57238473277440 z^(7/2) - 16834845081600 z^4 - 47692720373760 z^(9/2) - 3316415201280 z^5 - 10970386661376 z^(11/2) - 500095254528 z^6 - 1687116840960 z^(13/2) - 119185342464 z^7 - 489626271744 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-15652775985721875 + 5181608602170000 z - 1205901638323200 z^2 + 306260733542400 z^3 - 144122698137600 z^4 - 177381782323200 z^5 - 42046052106240 z^6 - 6407017463808 z^7 - 1971389988864 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-15652775985721875 + 5181608602170000 z - 1205901638323200 z^2 + 306260733542400 z^3 - 144122698137600 z^4 - 177381782323200 z^5 - 42046052106240 z^6 - 6407017463808 z^7 - 1971389988864 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (227994731135631360 z^(19/4)))

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]