Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0525)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=1

http://functions.wolfram.com/07.22.03.0525.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 1}, z] == (1/108056025) ((108056025 - 851288130 z + 944937648 z^2 - 227580192 z^3 + 15651840 z^4 - 341504 z^5 + 2048 z^6) BesselI[0, Sqrt[z]]^2 - 8 Sqrt[z] (-50737995 + 99683334 z - 27049608 z^2 + 1924896 z^3 - 42496 z^4 + 256 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + 2 z (255001671 - 420944760 z + 110002032 z^2 - 7741312 z^3 + 170240 z^4 - 1024 z^5) BesselI[1, Sqrt[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,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]