Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8178)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8178.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 17/4}, z] == (-4 z^(1/4) (-2624278338556875 - 3499037784742500 Sqrt[z] - 589311626904000 z + 1346998004352000 z^(3/2) - 239466311884800 z^2 - 1425913038950400 z^(5/2) + 232213983805440 z^3 - 1770590943313920 z^(7/2) + 124085126430720 z^4 - 1183801186713600 z^(9/2) - 311333643878400 z^5 + 1329019446362112 z^(11/2) + 30219524112384 z^6 - 122988804440064 z^(13/2) - 718333280256 z^7 + 2886218022912 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-2624278338556875 + 3499037784742500 Sqrt[z] - 589311626904000 z - 1346998004352000 z^(3/2) - 239466311884800 z^2 + 1425913038950400 z^(5/2) + 232213983805440 z^3 + 1770590943313920 z^(7/2) + 124085126430720 z^4 + 1183801186713600 z^(9/2) - 311333643878400 z^5 - 1329019446362112 z^(11/2) + 30219524112384 z^6 + 122988804440064 z^(13/2) - 718333280256 z^7 - 2886218022912 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2624278338556875 + 2209918600890000 z - 1885797206092800 z^2 + 6400281426739200 z^3 + 7314607344844800 z^4 + 5573034167500800 z^5 - 5404154344243200 z^6 + 494094111473664 z^7 - 11557756993536 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2624278338556875 + 2209918600890000 z - 1885797206092800 z^2 + 6400281426739200 z^3 + 7314607344844800 z^4 + 5573034167500800 z^5 - 5404154344243200 z^6 + 494094111473664 z^7 - 11557756993536 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(37405385576939520 z^(13/4))

Standard Form

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MathML Form

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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]