Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2637)

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=-11/2, a₂>=-11/2

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

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

http://functions.wolfram.com/07.25.03.2637.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {-(7/2), 6}, z] == (1/(32081724675 z^3)) (32 E^(z/2) (-3032429400 + 1984457475 z - 856215360 z^2 + 1341204480 z^3 + 745113600 z^4 + 407715840 z^5 + 316538880 z^6 + 648019968 z^7 - 1094713344 z^8 + 167772160 z^9) BesselI[0, z/2]) - (1/(32081724675 z^4)) (32 E^(z/2) (-12129717600 + 7937829900 z - 3803915115 z^2 + 1602659520 z^3 - 894136320 z^4 - 519321600 z^5 - 266649600 z^6 - 174194688 z^7 - 195035136 z^8 - 926941184 z^9 + 167772160 z^10) BesselI[1, z/2])

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]