Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8087)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.8087.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), 21/4}, -z] == (221 (Sqrt[Pi] (5613331366173155625 + 2228617912128300000 z + 660331233223200000 z^2 + 244992457543680000 z^3 + 361041516380160000 z^4 - 154044380322201600 z^5 + 26674351570944000 z^6 - 3167269945344000 z^7 + 422302659379200 z^8 + 79027398246400 z^9 + 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-5613331366173155625 + 3758935545123066000 z + 196212709300608000 z^2 + 25771933845504000 z^3 - 11096232660172800 z^4 + 1823338974412800 z^5 - 206733217628160 z^6 + 22017076101120 z^7 + 4874787880960 z^8 + 68719476736 z^9)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (1871110455391051875 - 112492142231238000 z + 18752263592832000 z^2 + 24584091627110400 z^3 - 9978678381772800 z^4 + 1704679597670400 z^5 - 201051781201920 z^6 + 25495999610880 z^7 + 4926327488512 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(93097848547049472000 z^(17/4))

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]