Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6830)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-21/4

http://functions.wolfram.com/07.22.03.6830.01

Input Form

HypergeometricPFQ[{3}, {-(21/4), 21/4}, z] == (1/(344064 z^(17/4))) ((-8 E^(2 Sqrt[z]) z^(1/4) (76603301775 + 27539972460 z + 4454049600 z^2 + 302702400 z^3 + 9224448 z^4 + 93184 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (76603301775 - 153206603550 Sqrt[z] + 150105255300 z - 95935039200 z^(3/2) + 44886441600 z^2 - 16332956640 z^(5/2) + 4782697920 z^3 - 1146562560 z^(7/2) + 225434880 z^4 - 35735040 z^(9/2) + 4359168 z^5 - 368640 z^(11/2) + 16384 z^6) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (76603301775 + 153206603550 Sqrt[z] + 150105255300 z + 95935039200 z^(3/2) + 44886441600 z^2 + 16332956640 z^(5/2) + 4782697920 z^3 + 1146562560 z^(7/2) + 225434880 z^4 + 35735040 z^(9/2) + 4359168 z^5 + 368640 z^(11/2) + 16384 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</semantics> </math>

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]