Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9960)

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`=-1/2

http://functions.wolfram.com/07.22.03.9960.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), 23/4}, z] == -((19 (4 z^(1/4) (1662432759862875 + 2216577013150500 Sqrt[z] + 1013292348868800 z - 100185292247040 z^2 + 47340302929920 z^(5/2) + 15243746918400 z^3 - 45166657536000 z^(7/2) + 31616660275200 z^4 - 93424540188672 z^(9/2) + 32359764197376 z^5 - 154866454364160 z^(11/2) - 9870237499392 z^6 + 40779909169152 z^(13/2) + 447750340608 z^7 - 1803886264320 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-1662432759862875 + 2216577013150500 Sqrt[z] - 1013292348868800 z + 100185292247040 z^2 + 47340302929920 z^(5/2) - 15243746918400 z^3 - 45166657536000 z^(7/2) - 31616660275200 z^4 - 93424540188672 z^(9/2) - 32359764197376 z^5 - 154866454364160 z^(11/2) + 9870237499392 z^6 + 40779909169152 z^(13/2) - 447750340608 z^7 - 1803886264320 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1662432759862875 + 759969261651600 z - 260096431795200 z^2 + 106706228428800 z^3 - 94849980825600 z^4 - 303519938641920 z^5 - 647509202436096 z^6 + 164446781571072 z^7 - 7228429959168 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-1662432759862875 + 759969261651600 z - 260096431795200 z^2 + 106706228428800 z^3 - 94849980825600 z^4 - 303519938641920 z^5 - 647509202436096 z^6 + 164446781571072 z^7 - 7228429959168 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(26599385299156992 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]