Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a976)

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

For fixed z and a₁=-11/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a976.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 17/4}, z] == (1/(513382809600 z^(7/2))) ((4 (20437401600 - 13398791175 Sqrt[z] + 36634682700 z - 10176289200 z^(3/2) + 30539678400 z^2 - 8591869440 z^(5/2) + 40527083520 z^3 + 2386206720 z^(7/2) - 9855467520 z^4 - 107151360 z^(9/2) + 431751168 z^5 + 1048576 z^(11/2) - 4194304 z^6 + E^(4 Sqrt[z]) (-20437401600 - 13398791175 Sqrt[z] - 36634682700 z - 10176289200 z^(3/2) - 30539678400 z^2 - 8591869440 z^(5/2) - 40527083520 z^3 + 2386206720 z^(7/2) + 9855467520 z^4 - 107151360 z^(9/2) - 431751168 z^5 + 1048576 z^(11/2) + 4194304 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (54273594375 + 115783668000 z + 102918816000 z^2 + 168892416000 z^3 - 39739392000 z^4 + 1730150400 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (54273594375 + 115783668000 z + 102918816000 z^2 + 168892416000 z^3 - 39739392000 z^4 + 1730150400 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]