Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al3e)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, b₁>=-11/2

For fixed z and a₁=7/2, a₂=4, b₁=-7/2

http://functions.wolfram.com/07.25.03.al3e.01

Input Form

HypergeometricPFQ[{7/2, 4}, {-(7/2), -(5/2)}, z] == (1/70875) (70875 + 113400 z + 340200 z^2 + 4989600 z^3 - 227026800 z^4 - 2248646400 z^5 - 4257227520 z^6 - 3114915840 z^7 - 1108696320 z^8 - 212686080 z^9 - 22882560 z^10 - 1367424 z^11 - 41984 z^12 - 512 z^13) - (1/70875) (64 E^z Sqrt[Pi] (10810800 z^(9/2) + 56019600 z^(11/2) + 85087800 z^(13/2) + 56032200 z^(15/2) + 18830070 z^(17/2) + 3492090 z^(19/2) + 367905 z^(21/2) + 21690 z^(23/2) + 660 z^(25/2) + 8 z^(27/2)) Erf[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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]