Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am16)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.am16.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(5/2), -(3/2)}, z] == (1/14175) (14175 + 68040 z + 1247400 z^2 - 64864800 z^3 - 719999280 z^4 - 1487566080 z^5 - 1169715456 z^6 - 442851840 z^7 - 89692800 z^8 - 10130304 z^9 - 632640 z^10 - 20224 z^11 - 256 z^12) - (1/14175) (32 E^z Sqrt[Pi] (6486480 z^(7/2) + 36756720 z^(9/2) + 60245640 z^(11/2) + 42388920 z^(13/2) + 15104250 z^(15/2) + 2952054 z^(17/2) + 326151 z^(19/2) + 20082 z^(21/2) + 636 z^(23/2) + 8 z^(25/2)) 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]