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

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=-11/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 5}, z] == (1/(3094331625 z^2)) (32 E^(z/2) (1964187225 - 827026200 z + 354573450 z^2 - 200831400 z^3 + 131090400 z^4 - 93985920 z^5 + 80015040 z^6 - 97943040 z^7 + 312940800 z^8 + 844124160 z^9 + 457830912 z^10 + 99895296 z^11 + 10153984 z^12 + 475136 z^13 + 8192 z^14) BesselI[0, z/2]) + (1/(3094331625 z^3)) (64 E^(z/2) (-3928374450 + 1654052400 z - 638512875 z^2 + 143918775 z^3 + 7881300 z^4 - 31570560 z^5 + 27306720 z^6 - 22356000 z^7 + 22705920 z^8 - 38008320 z^9 + 254597376 z^10 + 185902848 z^11 + 45214720 z^12 + 4845568 z^13 + 233472 z^14 + 4096 z^15) 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]