Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a96i)

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.a96i.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, -(7/4)}, z] == (1/(267321600 z^(7/2))) ((723647925 - 723647925 E^(4 Sqrt[z]) + 1447295850 Sqrt[z] + 1447295850 E^(4 Sqrt[z]) Sqrt[z] + 1102701600 z - 1102701600 E^(4 Sqrt[z]) z + 275675400 z^(3/2) + 275675400 E^(4 Sqrt[z]) z^(3/2) - 64864800 z^2 + 64864800 E^(4 Sqrt[z]) z^2 + 17297280 z^(5/2) + 17297280 E^(4 Sqrt[z]) z^(5/2) - 5322240 z^3 + 5322240 E^(4 Sqrt[z]) z^3 + 1935360 z^(7/2) + 1935360 E^(4 Sqrt[z]) z^(7/2) - 860160 z^4 + 860160 E^(4 Sqrt[z]) z^4 + 491520 z^(9/2) + 491520 E^(4 Sqrt[z]) z^(9/2) - 393216 z^5 + 393216 E^(4 Sqrt[z]) z^5 + 524288 z^(11/2) + 524288 E^(4 Sqrt[z]) z^(11/2) - 2097152 z^6 + 2097152 E^(4 Sqrt[z]) z^6 - 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) Erf[Sqrt[2] z^(1/4)] - 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) 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]